SyncValsverifier → artifact → classifier → verdict
SyncVals · Trajectory

reverse-engineer-objectives

claude-code claude-opus-4-8 ✗ failed GOOD_FAILURE ↑ View task
Solved from the instruction alone, tests/ and solution/ were withheld from the agent's workspace and restored only for grading.
Reward = tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it.
Classification , post-hoc; cannot change the reward
GOOD_FAILUREHonest miss, the agent ran correctly but couldn't solve it. Expected for a hard task; the task is sound.
SubtypeIncomplete Understanding
EvidenceTest output: 'FUNCTIONS PASSED: 47/49 (partial_score=0.9592)' and 'REWARD = 0 (1 iff ALL 49 functions match the sealed reference exactly)'. Agent's trajectory shows they verified 49/49 functions locally (step 22: 'TOTAL: 49/49 pass. FAILS: []') but 2 functions failed on held-out inputs. The instruction explicitly states: 'Agreement on the inputs you happen to try does not imply agreement on the inputs you are graded on.'
Root causeThe agent successfully reverse-engineered and implemented 47 of 49 functions correctly, but their probing of the 2 failing functions was insufficient to discover all numerical conventions needed for exact agreement on the held-out test set. The agent's local verification did not catch edge cases or subtle numerical behaviors that only appeared in grading inputs.
RecommendationN/A - task is fine. The task clearly warns that local testing agreement doesn't guarantee grading agreement, and this is an expected outcome for a hard reverse-engineering challenge. The agent needed more comprehensive edge-case testing for those 2 functions, exploring boundary conditions, extreme values, special cases with each parameter, and multiple random seeds more exhaustively.
Trajectory
Tool-by-tool agent trajectory
28 tool calls · 5 tool types · 30 steps
Reimplement the post-training objectives library in `/app/objectives.py` so that every function reproduces the sealed reference module `reforacle` exactly. `reforacle` is importable and callable (`import reforacle`) but its source cannot be read. It is the only ground truth; there is no written specification of what any function computes or of the conventions it follows. Recover its behavior by calling it. `/app/objectives.py` contains forty-nine function stubs. Keep every signature exactly as given and implement every function. The names indicate the standard post-training quantity each is meant to produce, but the reference's exact definition is whatever `reforacle` returns , not what you assume. Determine each definition by probing. Grading compares your implementation to `reforacle` on held-out inputs you do not see, function by function, requiring exact numerical agreement (primitives within `atol=1e-6, rtol=1e-5`; composite objectives within `atol=1e-5, rtol=1e-4`). Each function passes only if it agrees on every graded input, and the task passes only if all forty-nine functions pass. Agreement on the inputs you happen to try does not imply agreement on the inputs you are graded on. Grading runs your `/app/objectives.py` in a clean sandbox that does not contain `reforacle`, so any submission that imports, wraps, calls, loads, or otherwise depends on the reference at run time fails outright. Your file must be a standalone implementation whose only dependency is `torch`. Do not read, decompile, disassemble, or otherwise extract the compiled reference; recover its behavior only by calling it and comparing. `python3 /app/probe.py` shows the calling pattern; `bash /app/timer.sh` reports remaining budget.

/app/objectives.py

contents
1	from __future__ import annotations
2	
3	import torch
4	
5	
6	def masked_mean(values, mask, axis=None):
7	    raise NotImplementedError
8	
9	
10	def masked_sum(values, mask, axis=None):
11	    raise NotImplementedError
12	
13	
14	def logsumexp(x, axis):
15	    raise NotImplementedError
16	
17	
18	def log_softmax(x, axis):
19	    raise NotImplementedError
20	
21	
22	def selective_logprobs(logits, labels, mask):
23	    raise NotImplementedError
24	
25	
26	def token_logprobs(logits, labels):
27	    raise NotImplementedError
28	
29	
30	def sequence_logprob(logits, labels, mask, length_normalize):
31	    raise NotImplementedError
32	
33	
34	def entropy(logits, mask):
35	    raise NotImplementedError
36	
37	
38	def dpo_loss(pc, pr, rc, rr, beta, label_smoothing):
39	    raise NotImplementedError
40	
41	
42	def ipo_loss(pc, pr, rc, rr, beta):
43	    raise NotImplementedError
44	
45	
46	def grpo_advantages(rewards, group_size, scale_by_std):
47	    raise NotImplementedError
48	
49	
50	def gae(rewards, values, next_value, gamma, lam):
51	    raise NotImplementedError
52	
53	
54	def kl_penalty(logp, ref_logp, estimator):
55	    raise NotImplementedError
56	
57	
58	def clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
59	    raise NotImplementedError
60	
61	
62	def value_loss(values, old_values, returns, clip):
63	    raise NotImplementedError
64	
65	
66	def whiten(values, mask, shift_mean):
67	    raise NotImplementedError
68	
69	
70	def dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,
71	                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,
72	                      beta, label_smoothing):
73	    raise NotImplementedError
74	
75	
76	def grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,
77	                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,
78	                   kl_estimator):
79	    raise NotImplementedError
80	
81	
82	def ppo_objective(rewards, values, old_values, logp, old_logp, next_value,
83	                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):
84	    raise NotImplementedError
85	
86	
87	def rloo_advantages(rewards, group_size):
88	    raise NotImplementedError
89	
90	
91	def reverse_kl(logp, ref_logp):
92	    raise NotImplementedError
93	
94	
95	def importance_ratio(logp, old_logp, clip):
96	    raise NotImplementedError
97	
98	
99	def discounted_returns(rewards, gamma):
100	    raise NotImplementedError
101	
102	
103	def normalize(x, eps):
104	    raise NotImplementedError
105	
106	
107	def top_p_mask(probs, p):
108	    raise NotImplementedError
109	
110	
111	def smoothed_nll(logits, labels, smoothing):
112	    raise NotImplementedError
113	
114	
115	def bradley_terry_logit(chosen_reward, rejected_reward, beta):
116	    raise NotImplementedError
117	
118	
119	def rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):
120	    raise NotImplementedError
121	
122	
123	def reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):
124	    raise NotImplementedError
125	
126	
127	def cross_entropy(logits, labels, ignore_index):
128	    raise NotImplementedError
129	
130	
131	def top_k_mask(logits, k):
132	    raise NotImplementedError
133	
134	
135	def group_mean_baseline(rewards, group_size):
136	    raise NotImplementedError
137	
138	
139	def lambda_returns(rewards, values, next_value, gamma, lam):
140	    raise NotImplementedError
141	
142	
143	def symmetric_kl(logp, ref_logp):
144	    raise NotImplementedError
145	
146	
147	def huber_value_loss(values, returns, delta):
148	    raise NotImplementedError
149	
150	
151	def normalized_entropy(logits, mask):
152	    raise NotImplementedError
153	
154	
155	def clip_fraction(logp, old_logp, clip):
156	    raise NotImplementedError
157	
158	
159	def masked_whiten(values, mask, shift_mean):
160	    raise NotImplementedError
161	
162	
163	def logprob_at_temperature(logits, labels, temperature):
164	    raise NotImplementedError
165	
166	
167	def advantage_mean_std(advantages, mask):
168	    raise NotImplementedError
169	
170	
171	def argmax_tokens(logits):
172	    raise NotImplementedError
173	
174	
175	def mode_label(labels):
176	    raise NotImplementedError
177	
178	
179	def median_reward(rewards):
180	    raise NotImplementedError
181	
182	
183	def masked_max(values, mask):
184	    raise NotImplementedError
185	
186	
187	def quantile_lower(x, q):
188	    raise NotImplementedError
189	
190	
191	def pad_mask_from_lengths(lengths, max_len):
192	    raise NotImplementedError
193	
194	
195	def first_nonzero_index(mask):
196	    raise NotImplementedError
197	
198	
199	def cumulative_max(x):
200	    raise NotImplementedError
201	
202	
203	def bucketize_reward(rewards, boundaries):
204	    raise NotImplementedError
205

1	from __future__ import annotations
2	
3	import torch
4	
5	import reforacle
6	
7	g = torch.Generator().manual_seed(0)
8	values = torch.randn(8, generator=g)
9	mask = (torch.rand(8, generator=g) > 0.5).float()
10	
11	print("inputs:")
12	print("  values =", values.tolist())
13	print("  mask   =", mask.tolist())
14	print("reference masked_mean ->", reforacle.masked_mean(values, mask).item())
15	print("reference masked_mean (empty mask) ->", reforacle.masked_mean(torch.randn(4, generator=g), torch.zeros(4)).item())
16	print()
17	print("Probe any reference function this way to discover its exact numerical")
18	print("convention, then implement it in /app/objectives.py to match.")
19

Remaining time (hours:minutes):
1:59

[stdout]
Remaining time (hours:minutes):
1:59

/app/probe.py

contents
1	from __future__ import annotations
2	
3	import torch
4	
5	
6	def masked_mean(values, mask, axis=None):
7	    raise NotImplementedError
8	
9	
10	def masked_sum(values, mask, axis=None):
11	    raise NotImplementedError
12	
13	
14	def logsumexp(x, axis):
15	    raise NotImplementedError
16	
17	
18	def log_softmax(x, axis):
19	    raise NotImplementedError
20	
21	
22	def selective_logprobs(logits, labels, mask):
23	    raise NotImplementedError
24	
25	
26	def token_logprobs(logits, labels):
27	    raise NotImplementedError
28	
29	
30	def sequence_logprob(logits, labels, mask, length_normalize):
31	    raise NotImplementedError
32	
33	
34	def entropy(logits, mask):
35	    raise NotImplementedError
36	
37	
38	def dpo_loss(pc, pr, rc, rr, beta, label_smoothing):
39	    raise NotImplementedError
40	
41	
42	def ipo_loss(pc, pr, rc, rr, beta):
43	    raise NotImplementedError
44	
45	
46	def grpo_advantages(rewards, group_size, scale_by_std):
47	    raise NotImplementedError
48	
49	
50	def gae(rewards, values, next_value, gamma, lam):
51	    raise NotImplementedError
52	
53	
54	def kl_penalty(logp, ref_logp, estimator):
55	    raise NotImplementedError
56	
57	
58	def clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
59	    raise NotImplementedError
60	
61	
62	def value_loss(values, old_values, returns, clip):
63	    raise NotImplementedError
64	
65	
66	def whiten(values, mask, shift_mean):
67	    raise NotImplementedError
68	
69	
70	def dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,
71	                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,
72	                      beta, label_smoothing):
73	    raise NotImplementedError
74	
75	
76	def grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,
77	                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,
78	                   kl_estimator):
79	    raise NotImplementedError
80	
81	
82	def ppo_objective(rewards, values, old_values, logp, old_logp, next_value,
83	                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):
84	    raise NotImplementedError
85	
86	
87	def rloo_advantages(rewards, group_size):
88	    raise NotImplementedError
89	
90	
91	def reverse_kl(logp, ref_logp):
92	    raise NotImplementedError
93	
94	
95	def importance_ratio(logp, old_logp, clip):
96	    raise NotImplementedError
97	
98	
99	def discounted_returns(rewards, gamma):
100	    raise NotImplementedError
101	
102	
103	def normalize(x, eps):
104	    raise NotImplementedError
105	
106	
107	def top_p_mask(probs, p):
108	    raise NotImplementedError
109	
110	
111	def smoothed_nll(logits, labels, smoothing):
112	    raise NotImplementedError
113	
114	
115	def bradley_terry_logit(chosen_reward, rejected_reward, beta):
116	    raise NotImplementedError
117	
118	
119	def rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):
120	    raise NotImplementedError
121	
122	
123	def reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):
124	    raise NotImplementedError
125	
126	
127	def cross_entropy(logits, labels, ignore_index):
128	    raise NotImplementedError
129	
130	
131	def top_k_mask(logits, k):
132	    raise NotImplementedError
133	
134	
135	def group_mean_baseline(rewards, group_size):
136	    raise NotImplementedError
137	
138	
139	def lambda_returns(rewards, values, next_value, gamma, lam):
140	    raise NotImplementedError
141	
142	
143	def symmetric_kl(logp, ref_logp):
144	    raise NotImplementedError
145	
146	
147	def huber_value_loss(values, returns, delta):
148	    raise NotImplementedError
149	
150	
151	def normalized_entropy(logits, mask):
152	    raise NotImplementedError
153	
154	
155	def clip_fraction(logp, old_logp, clip):
156	    raise NotImplementedError
157	
158	
159	def masked_whiten(values, mask, shift_mean):
160	    raise NotImplementedError
161	
162	
163	def logprob_at_temperature(logits, labels, temperature):
164	    raise NotImplementedError
165	
166	
167	def advantage_mean_std(advantages, mask):
168	    raise NotImplementedError
169	
170	
171	def argmax_tokens(logits):
172	    raise NotImplementedError
173	
174	
175	def mode_label(labels):
176	    raise NotImplementedError
177	
178	
179	def median_reward(rewards):
180	    raise NotImplementedError
181	
182	
183	def masked_max(values, mask):
184	    raise NotImplementedError
185	
186	
187	def quantile_lower(x, q):
188	    raise NotImplementedError
189	
190	
191	def pad_mask_from_lengths(lengths, max_len):
192	    raise NotImplementedError
193	
194	
195	def first_nonzero_index(mask):
196	    raise NotImplementedError
197	
198	
199	def cumulative_max(x):
200	    raise NotImplementedError
201	
202	
203	def bucketize_reward(rewards, boundaries):
204	    raise NotImplementedError
205

1	from __future__ import annotations
2	
3	import torch
4	
5	import reforacle
6	
7	g = torch.Generator().manual_seed(0)
8	values = torch.randn(8, generator=g)
9	mask = (torch.rand(8, generator=g) > 0.5).float()
10	
11	print("inputs:")
12	print("  values =", values.tolist())
13	print("  mask   =", mask.tolist())
14	print("reference masked_mean ->", reforacle.masked_mean(values, mask).item())
15	print("reference masked_mean (empty mask) ->", reforacle.masked_mean(torch.randn(4, generator=g), torch.zeros(4)).item())
16	print()
17	print("Probe any reference function this way to discover its exact numerical")
18	print("convention, then implement it in /app/objectives.py to match.")
19

Remaining time (hours:minutes):
1:59

[stdout]
Remaining time (hours:minutes):
1:59

Check remaining budget

shell
bash /app/timer.sh
output
1	from __future__ import annotations
2	
3	import torch
4	
5	
6	def masked_mean(values, mask, axis=None):
7	    raise NotImplementedError
8	
9	
10	def masked_sum(values, mask, axis=None):
11	    raise NotImplementedError
12	
13	
14	def logsumexp(x, axis):
15	    raise NotImplementedError
16	
17	
18	def log_softmax(x, axis):
19	    raise NotImplementedError
20	
21	
22	def selective_logprobs(logits, labels, mask):
23	    raise NotImplementedError
24	
25	
26	def token_logprobs(logits, labels):
27	    raise NotImplementedError
28	
29	
30	def sequence_logprob(logits, labels, mask, length_normalize):
31	    raise NotImplementedError
32	
33	
34	def entropy(logits, mask):
35	    raise NotImplementedError
36	
37	
38	def dpo_loss(pc, pr, rc, rr, beta, label_smoothing):
39	    raise NotImplementedError
40	
41	
42	def ipo_loss(pc, pr, rc, rr, beta):
43	    raise NotImplementedError
44	
45	
46	def grpo_advantages(rewards, group_size, scale_by_std):
47	    raise NotImplementedError
48	
49	
50	def gae(rewards, values, next_value, gamma, lam):
51	    raise NotImplementedError
52	
53	
54	def kl_penalty(logp, ref_logp, estimator):
55	    raise NotImplementedError
56	
57	
58	def clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
59	    raise NotImplementedError
60	
61	
62	def value_loss(values, old_values, returns, clip):
63	    raise NotImplementedError
64	
65	
66	def whiten(values, mask, shift_mean):
67	    raise NotImplementedError
68	
69	
70	def dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,
71	                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,
72	                      beta, label_smoothing):
73	    raise NotImplementedError
74	
75	
76	def grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,
77	                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,
78	                   kl_estimator):
79	    raise NotImplementedError
80	
81	
82	def ppo_objective(rewards, values, old_values, logp, old_logp, next_value,
83	                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):
84	    raise NotImplementedError
85	
86	
87	def rloo_advantages(rewards, group_size):
88	    raise NotImplementedError
89	
90	
91	def reverse_kl(logp, ref_logp):
92	    raise NotImplementedError
93	
94	
95	def importance_ratio(logp, old_logp, clip):
96	    raise NotImplementedError
97	
98	
99	def discounted_returns(rewards, gamma):
100	    raise NotImplementedError
101	
102	
103	def normalize(x, eps):
104	    raise NotImplementedError
105	
106	
107	def top_p_mask(probs, p):
108	    raise NotImplementedError
109	
110	
111	def smoothed_nll(logits, labels, smoothing):
112	    raise NotImplementedError
113	
114	
115	def bradley_terry_logit(chosen_reward, rejected_reward, beta):
116	    raise NotImplementedError
117	
118	
119	def rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):
120	    raise NotImplementedError
121	
122	
123	def reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):
124	    raise NotImplementedError
125	
126	
127	def cross_entropy(logits, labels, ignore_index):
128	    raise NotImplementedError
129	
130	
131	def top_k_mask(logits, k):
132	    raise NotImplementedError
133	
134	
135	def group_mean_baseline(rewards, group_size):
136	    raise NotImplementedError
137	
138	
139	def lambda_returns(rewards, values, next_value, gamma, lam):
140	    raise NotImplementedError
141	
142	
143	def symmetric_kl(logp, ref_logp):
144	    raise NotImplementedError
145	
146	
147	def huber_value_loss(values, returns, delta):
148	    raise NotImplementedError
149	
150	
151	def normalized_entropy(logits, mask):
152	    raise NotImplementedError
153	
154	
155	def clip_fraction(logp, old_logp, clip):
156	    raise NotImplementedError
157	
158	
159	def masked_whiten(values, mask, shift_mean):
160	    raise NotImplementedError
161	
162	
163	def logprob_at_temperature(logits, labels, temperature):
164	    raise NotImplementedError
165	
166	
167	def advantage_mean_std(advantages, mask):
168	    raise NotImplementedError
169	
170	
171	def argmax_tokens(logits):
172	    raise NotImplementedError
173	
174	
175	def mode_label(labels):
176	    raise NotImplementedError
177	
178	
179	def median_reward(rewards):
180	    raise NotImplementedError
181	
182	
183	def masked_max(values, mask):
184	    raise NotImplementedError
185	
186	
187	def quantile_lower(x, q):
188	    raise NotImplementedError
189	
190	
191	def pad_mask_from_lengths(lengths, max_len):
192	    raise NotImplementedError
193	
194	
195	def first_nonzero_index(mask):
196	    raise NotImplementedError
197	
198	
199	def cumulative_max(x):
200	    raise NotImplementedError
201	
202	
203	def bucketize_reward(rewards, boundaries):
204	    raise NotImplementedError
205

1	from __future__ import annotations
2	
3	import torch
4	
5	import reforacle
6	
7	g = torch.Generator().manual_seed(0)
8	values = torch.randn(8, generator=g)
9	mask = (torch.rand(8, generator=g) > 0.5).float()
10	
11	print("inputs:")
12	print("  values =", values.tolist())
13	print("  mask   =", mask.tolist())
14	print("reference masked_mean ->", reforacle.masked_mean(values, mask).item())
15	print("reference masked_mean (empty mask) ->", reforacle.masked_mean(torch.randn(4, generator=g), torch.zeros(4)).item())
16	print()
17	print("Probe any reference function this way to discover its exact numerical")
18	print("convention, then implement it in /app/objectives.py to match.")
19

Remaining time (hours:minutes):
1:59

[stdout]
Remaining time (hours:minutes):
1:59

Run probe.py

shell
python3 probe.py 2>&1 | head -30
output
inputs:
  values = [1.5409960746765137, -0.293428897857666, -2.1787893772125244, 0.5684312582015991, -1.0845223665237427, -1.3985954523086548, 0.40334683656692505, 0.8380263447761536]
  mask   = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0]
reference masked_mean -> -0.07950486242771149
reference masked_mean (empty mask) -> 0.0

Probe any reference function this way to discover its exact numerical
convention, then implement it in /app/objectives.py to match.

[stdout]
inputs:
  values = [1.5409960746765137, -0.293428897857666, -2.1787893772125244, 0.5684312582015991, -1.0845223665237427, -1.3985954523086548, 0.40334683656692505, 0.8380263447761536]
  mask   = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0]
reference masked_mean -> -0.07950486242771149
reference masked_mean (empty mask) -> 0.0

Probe any reference function this way to discover its exact numerical
convention, then implement it in /app/objectives.py to match.
['F', 'advantage_mean_std', 'argmax_tokens', 'bradley_terry_logit', 'bucketize_reward', 'clip_fraction', 'clipped_pg_loss', 'cross_entropy', 'cumulative_max', 'discounted_returns', 'dpo_loss', 'dpo_sequence_loss', 'entropy', 'first_nonzero_index', 'gae', 'group_mean_baseline', 'grpo_advantages', 'grpo_objective', 'huber_value_loss', 'importance_ratio', 'ipo_loss', 'kl_penalty', 'lambda_returns', 'log_softmax', 'logprob_at_temperature', 'logsumexp', 'masked_max', 'masked_mean', 'masked_sum', 'masked_whiten', 'median_reward', 'mode_label', 'normalize', 'normalized_entropy', 'pad_mask_from_lengths', 'ppo_objective', 'quantile_lower', 'reverse_kl', 'reverse_kl_objective', 'rloo_advantages', 'rloo_objective', 'selective_logprobs', 'sequence_logprob', 'smoothed_nll', 'symmetric_kl', 'token_logprobs', 'top_k_mask', 'top_p_mask', 'torch', 'value_loss', 'whiten']

[stdout]
['F', 'advantage_mean_std', 'argmax_tokens', 'bradley_terry_logit', 'bucketize_reward', 'clip_fraction', 'clipped_pg_loss', 'cross_entropy', 'cumulative_max', 'discounted_returns', 'dpo_loss', 'dpo_sequence_loss', 'entropy', 'first_nonzero_index', 'gae', 'group_mean_baseline', 'grpo_advantages', 'grpo_objective', 'huber_value_loss', 'importance_ratio', 'ipo_loss', 'kl_penalty', 'lambda_returns', 'log_softmax', 'logprob_at_temperature', 'logsumexp', 'masked_max', 'masked_mean', 'masked_sum', 'masked_whiten', 'median_reward', 'mode_label', 'normalize', 'normalized_entropy', 'pad_mask_from_lengths', 'ppo_objective', 'quantile_lower', 'reverse_kl', 'reverse_kl_objective', 'rloo_advantages', 'rloo_objective', 'selective_logprobs', 'sequence_logprob', 'smoothed_nll', 'symmetric_kl', 'token_logprobs', 'top_k_mask', 'top_p_mask', 'torch', 'value_loss', 'whiten']

List reforacle attributes

shell
python3 -c "import reforacle; print([x for x in dir(reforacle) if not x.startswith('__')])"
output
inputs:
  values = [1.5409960746765137, -0.293428897857666, -2.1787893772125244, 0.5684312582015991, -1.0845223665237427, -1.3985954523086548, 0.40334683656692505, 0.8380263447761536]
  mask   = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0]
reference masked_mean -> -0.07950486242771149
reference masked_mean (empty mask) -> 0.0

Probe any reference function this way to discover its exact numerical
convention, then implement it in /app/objectives.py to match.

[stdout]
inputs:
  values = [1.5409960746765137, -0.293428897857666, -2.1787893772125244, 0.5684312582015991, -1.0845223665237427, -1.3985954523086548, 0.40334683656692505, 0.8380263447761536]
  mask   = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0]
reference masked_mean -> -0.07950486242771149
reference masked_mean (empty mask) -> 0.0

Probe any reference function this way to discover its exact numerical
convention, then implement it in /app/objectives.py to match.
['F', 'advantage_mean_std', 'argmax_tokens', 'bradley_terry_logit', 'bucketize_reward', 'clip_fraction', 'clipped_pg_loss', 'cross_entropy', 'cumulative_max', 'discounted_returns', 'dpo_loss', 'dpo_sequence_loss', 'entropy', 'first_nonzero_index', 'gae', 'group_mean_baseline', 'grpo_advantages', 'grpo_objective', 'huber_value_loss', 'importance_ratio', 'ipo_loss', 'kl_penalty', 'lambda_returns', 'log_softmax', 'logprob_at_temperature', 'logsumexp', 'masked_max', 'masked_mean', 'masked_sum', 'masked_whiten', 'median_reward', 'mode_label', 'normalize', 'normalized_entropy', 'pad_mask_from_lengths', 'ppo_objective', 'quantile_lower', 'reverse_kl', 'reverse_kl_objective', 'rloo_advantages', 'rloo_objective', 'selective_logprobs', 'sequence_logprob', 'smoothed_nll', 'symmetric_kl', 'token_logprobs', 'top_k_mask', 'top_p_mask', 'torch', 'value_loss', 'whiten']

[stdout]
['F', 'advantage_mean_std', 'argmax_tokens', 'bradley_terry_logit', 'bucketize_reward', 'clip_fraction', 'clipped_pg_loss', 'cross_entropy', 'cumulative_max', 'discounted_returns', 'dpo_loss', 'dpo_sequence_loss', 'entropy', 'first_nonzero_index', 'gae', 'group_mean_baseline', 'grpo_advantages', 'grpo_objective', 'huber_value_loss', 'importance_ratio', 'ipo_loss', 'kl_penalty', 'lambda_returns', 'log_softmax', 'logprob_at_temperature', 'logsumexp', 'masked_max', 'masked_mean', 'masked_sum', 'masked_whiten', 'median_reward', 'mode_label', 'normalize', 'normalized_entropy', 'pad_mask_from_lengths', 'ppo_objective', 'quantile_lower', 'reverse_kl', 'reverse_kl_objective', 'rloo_advantages', 'rloo_objective', 'selective_logprobs', 'sequence_logprob', 'smoothed_nll', 'symmetric_kl', 'token_logprobs', 'top_k_mask', 'top_p_mask', 'torch', 'value_loss', 'whiten']
write · /app/harness.py
"""Shared comparison harness for probing reforacle against a candidate impl.

Usage:
    from harness import compare
    compare(reforacle.masked_mean, my_masked_mean, make_inputs)

where make_inputs() returns a tuple of args (called many times, should use
fresh random tensors each call).
"""
from __future__ import annotations

import traceback
import torch


def _close(a, b, atol=1e-6, rtol=1e-5):
    if isinstance(a, (tuple, list)):
        if not isinstance(b, (tuple, list)) or len(a) != len(b):
            return False, "structure mismatch"
        for x, y in zip(a, b):
            ok, msg = _close(x, y, atol, rtol)
            if not ok:
                return False, msg
        return True, ""
    a = torch.as_tensor(a) if not torch.is_tensor(a) else a
    b = torch.as_tensor(b) if not torch.is_tensor(b) else b
    a = a.to(torch.float64) if a.is_floating_point() else a
    b = b.to(torch.float64) if b.is_floating_point() else b
    if a.shape != b.shape:
        return False, f"shape {tuple(a.shape)} vs {tuple(b.shape)}"
    if torch.allclose(a.float(), b.float(), atol=atol, rtol=rtol, equal_nan=True):
        return True, ""
    diff = (a.float() - b.float()).abs()
    return False, f"maxdiff={diff.max().item():.3e} ref={a.flatten()[:6].tolist()} got={b.flatten()[:6].tolist()}"


def compare(ref_fn, cand_fn, make_inputs, n=200, atol=1e-6, rtol=1e-5, verbose=True):
    fails = 0
    first_msg = ""
    for i in range(n):
        args = make_inputs()
        if not isinstance(args, tuple):
            args = (args,)
        try:
            r = ref_fn(*[a.clone() if torch.is_tensor(a) else a for a in args])
        except Exception as e:
            r = ("EXC", type(e).__name__, str(e))
        try:
            c = cand_fn(*[a.clone() if torch.is_tensor(a) else a for a in args])
        except Exception as e:
            c = ("EXC", type(e).__name__, str(e) + "\n" + traceback.format_exc())
        # exception match
        if isinstance(r, tuple) and len(r) and r[0] == "EXC":
            if isinstance(c, tuple) and len(c) and c[0] == "EXC" and c[1] == r[1]:
                continue
            fails += 1
            if not first_msg:
                first_msg = f"ref raised {r[1]}:{r[2]} but cand -> {c}"
            continue
        if isinstance(c, tuple) and len(c) and c[0] == "EXC":
            fails += 1
            if not first_msg:
                first_msg = f"cand raised: {c[1]}:{c[2]}"
            continue
        ok, msg = _close(r, c, atol, rtol)
        if not ok:
            fails += 1
            if not first_msg:
                first_msg = f"[iter {i}] {msg}\n args={[a.tolist() if torch.is_tensor(a) else a for a in args]}"
    if verbose:
        if fails == 0:
            print(f"  PASS ({n}/{n})")
        else:
            print(f"  FAIL {fails}/{n}: {first_msg}")
    return fails == 0

Probe reduction conventions

shell
python3 -c "
import torch, reforacle as R
g=torch.Generator().manual_seed(1)
# masked_mean axis behavior
v=torch.randn(3,4,generator=g); m=(torch.rand(3,4,generator=g)>0.4).float()
print('mm axis=1', R.masked_mean(v,m,axis=1))
print('mm axis=0', R.masked_mean(v,m,axis=0))
print('ms axis=1', R.masked_sum(v,m,axis=1))
print('lse', R.logsumexp(v,axis=1))
print('logsoftmax shape', R.log_softmax(v,axis=1).shape)
# normalize
x=torch.randn(5,generator=g)
print('normalize eps', R.normalize(x,1e-5))
print('normalize mean/std', x.mean().item(), x.std().item(), x.std(unbiased=False).item())
"
output
mm axis=1 tensor([ 0.3166, -0.4357, -1.0276])
mm axis=0 tensor([-1.0276, 0.0504, -0.7305, 0.5015])
ms axis=1 tensor([ 0.9499, -1.3072, -1.0276])
lse tensor([1.8194, 1.1525, 0.8244])
logsoftmax shape torch.Size([3, 4])
normalize eps tensor([-0.8368, -0.1999, 1.4305, -0.9505, 0.5568])
normalize mean/std 0.3316972851753235 2.275648832321167 2.0354020595550537

[stdout]
mm axis=1 tensor([ 0.3166, -0.4357, -1.0276])
mm axis=0 tensor([-1.0276, 0.0504, -0.7305, 0.5015])
ms axis=1 tensor([ 0.9499, -1.3072, -1.0276])
lse tensor([1.8194, 1.1525, 0.8244])
logsoftmax shape torch.Size([3, 4])
normalize eps tensor([-0.8368, -0.1999, 1.4305, -0.9505, 0.5568])
normalize mean/std 0.3316972851753235 2.275648832321167 2.0354020595550537

Determine normalize convention

shell
python3 -c "
import torch, reforacle as R
g=torch.Generator().manual_seed(1)
x=torch.tensor([0.3316972851753235])  # placeholder
# recompute normalize precisely
xx=torch.randn(5,generator=torch.Generator().manual_seed(1))
# need same x as before: regenerate sequence
g2=torch.Generator().manual_seed(1)
v=torch.randn(3,4,generator=g2); m=(torch.rand(3,4,generator=g2)>0.4).float()
x=torch.randn(5,generator=g2)
print('x',x.tolist())
print('ref', R.normalize(x,1e-5).tolist())
mean=x.mean()
print('unb',((x-mean)/(x.std()+1e-5)).tolist())
print('bia',((x-mean)/(x.std(unbiased=False)+1e-5)).tolist())
print('sqrtvar',((x-mean)/torch.sqrt(x.var(unbiased=False)+1e-5)).tolist())
"
output
x [-1.5726652145385742, -0.12324775755405426, 3.586989402770996, -1.8312901258468628, 1.5987002849578857]
ref [-0.836840033531189, -0.19991794228553772, 1.430483341217041, -0.9504884481430054, 0.5567631721496582]
unb [-0.836840033531189, -0.19991794228553772, 1.430483341217041, -0.9504884481430054, 0.5567631721496582]
bia [-0.9356151819229126, -0.22351494431495667, 1.5993282794952393, -1.0626779794692993, 0.6224798560142517]
sqrtvar [-0.9356185793876648, -0.22351576387882233, 1.5993341207504272, -1.062681794166565, 0.6224821209907532]

[stdout]
x [-1.5726652145385742, -0.12324775755405426, 3.586989402770996, -1.8312901258468628, 1.5987002849578857]
ref [-0.836840033531189, -0.19991794228553772, 1.430483341217041, -0.9504884481430054, 0.5567631721496582]
unb [-0.836840033531189, -0.19991794228553772, 1.430483341217041, -0.9504884481430054, 0.5567631721496582]
bia [-0.9356151819229126, -0.22351494431495667, 1.5993282794952393, -1.0626779794692993, 0.6224798560142517]
sqrtvar [-0.9356185793876648, -0.22351576387882233, 1.5993341207504272, -1.062681794166565, 0.6224821209907532]
Agent
{
  "description": "Reverse-engineer logprob functions",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`) to reproduce its exact numerical behavior in pure `torch`. You CANNOT read source; only call and compare.\n\nHelper: `from harness import compare` at /app/harness.py , `compare(ref_fn, cand_fn, make_inputs, n=300)` (make_inputs returns tuple of args w/ fresh randoms) reports match at atol=1e-6, rtol=1e-5. Use heavily.\n\nImplement these 6 functions EXACTLY as reforacle. Probe carefully.\n\nSignatures (keep EXACTLY):\n```\ndef selective_logprobs(logits, labels, mask):   # log p(label) per position (log_softmax then gather), multiplied by mask? or masked-selected? PROBE output shape , per-position (mask applied as multiply) most likely\ndef token_logprobs(logits, labels):             # log_softmax(logits,-1).gather(labels); output shape = labels shape\ndef sequence_logprob(logits, labels, mask, length_normalize):  # sum over sequence of token logprobs*mask; if length_normalize divide by mask.sum(); PROBE per-batch shape, and whether length_normalize is bool\ndef smoothed_nll(logits, labels, smoothing):    # label-smoothed negative log likelihood. standard: (1-s)*nll + s*mean_over_vocab(-logprob). reduction? PROBE (mean over all? per-token?). Determine sign (positive loss).\ndef cross_entropy(logits, labels, ignore_index): # F.cross_entropy-like; reduction=mean over non-ignored; handle ignore_index. logits shape (N,V) labels (N)? or (N,T,V)? PROBE both. what if all ignored?\ndef logprob_at_temperature(logits, labels, temperature):  # log_softmax(logits/temperature) then gather labels\n```\n\nDetails to nail by probing:\n- Shapes: typical logits (batch, seq, vocab) or (batch, vocab). Try (B,T,V) with labels (B,T) and mask (B,T). Determine output shapes exactly.\n- token_logprobs: does it gather with labels.unsqueeze(-1) then squeeze , output = labels.shape. Confirm.\n- selective_logprobs vs token_logprobs difference: selective takes a mask. Determine if it returns logprobs*mask (same shape) or a summed/reduced value. PROBE by comparing output shape to inputs.\n- sequence_logprob length_normalize True/False: compute both, and check normalization denominator (mask.sum(-1)) and empty-mask behavior.\n- smoothed_nll: determine the exact smoothing formula and reduction. Standard label smoothing loss = (1-s)*(-logp_label) + s*(-mean_v logp_v). Check reduction (mean over batch?).\n- cross_entropy: match torch.nn.functional.cross_entropy(logits, labels, ignore_index=ignore_index) default reduction 'mean'. Verify for 2D and 3D (may need to permute to (N,V,...)).\n\nDeliverables:\n1. Write /app/part3.py: `import torch` (+`from __future__ import annotations`) + 6 pure-torch defs (NO reforacle import). You MAY use torch.nn.functional as F.\n2. Verify each with compare() n>=300 across shapes/edge cases; iterate to robust pass.\n3. Final message: FULL /app/part3.py source + per-function pass/fail.\n\nDo not modify /app/objectives.py.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 6 functions pass across shapes and edge cases. Done.\n\n## Summary\n\nReverse-engineered all 6 functions and wrote `/app/part3.py` (pure torch, no reforacle import). Verified each with `compare()` at n≥300 across (B,T,V) and (N,V) shapes plus edge cases.\n\n**Per-function results (all PASS):**\n\n| Function | Behavior discovered | Result |\n|---|---|---|\n| `token_logprobs` | `log_softmax(-1).gather(labels)` → shape = labels.shape | PASS 300/300 |\n| `selective_logprobs` | token logprobs × mask, then **sum over seq** → shape (B,) | PASS 300/300 |\n| `sequence_logprob` | sum of (logprob×mask) over seq; if `length_normalize` truthy, divide by `mask.sum(-1).clamp(min=1)` (empty mask → 0, not nan) | PASS (both flags + empty-mask) |\n| `smoothed_nll` | `(1-s)*nll + s*(-mean_v logp)` per token, reduced by **mean over all** → scalar | PASS 300/300 |\n| `cross_entropy` | log_softmax, gather on `labels.clamp(min=0)` (so `-100` is safe but an in-range out-of-vocab ignore_index still raises), mask by `labels!=ignore_index`, `sum/mask.sum().clamp(min=1)` → **all-ignored gives 0, not nan** (differs from `F.cross_entropy`). Works for 2D (N,V) and 3D (B,T,V) | PASS 300/300 + all-ignored |\n| `logprob_at_temperature` | `log_softmax(logits/temperature,-1).gather(labels)` | PASS 300/300 |\n\n**Key non-obvious findings:**\n- `selective_logprobs` is a *reduced* value (sum over sequence), shape (B,), not element-wise like `token_logprobs`.\n- `sequence_logprob` normalizes with a `clamp(min=1)` denominator, so empty masks yield 0 rather than nan.\n- `cross_entropy` does **not** wrap `F.cross_entropy`: it clamps negatives before gather and uses a `clamp(min=1)` denominator, giving **0 for the all-ignored case** where `F.cross_entropy` returns nan.\n\nFull source is at `/app/part3.py`."}

{"type": "text", "text": "agentId: a579217cf7f7f4bf4 (use SendMessage with to: 'a579217cf7f7f4bf4', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 23434\ntool_uses: 16\nduration_ms: 150042</usage>"}

{"type": "text", "text": "All edge cases pass across 2D/3D shapes, extreme values, boundary conditions, clip=None, all-mask, and varied label_smoothing/delta/clip values.\n\n## Summary\n\nI reverse-engineered all 11 `reforacle` functions by probing and verified each with `compare()` at n≥300 (many at 400-500), plus extensive edge-case runs. **All 11 functions PASS.**\n\n### Deliverable: `/app/part5.py`\n\n```python\nfrom __future__ import annotations\n\nimport torch\nimport torch.nn.functional as F\n\n\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):\n    logits = beta * ((pc - rc) - (pr - rr))\n    ls = label_smoothing\n    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)\n    return loss.mean()\n\n\ndef ipo_loss(pc, pr, rc, rr, beta):\n    logits = (pc - rc) - (pr - rr)\n    loss = (logits - 1.0 / (2.0 * beta)) ** 2\n    return loss.mean()\n\n\ndef kl_penalty(logp, ref_logp, estimator):\n    d = logp - ref_logp\n    if estimator == \"k1\":\n        return d\n    if estimator == \"k2\":\n        return 0.5 * d * d\n    if estimator == \"k3\":\n        return torch.exp(-d) - 1.0 + d\n    raise ValueError(estimator)\n\n\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):\n    ratio = torch.exp(logp - old_logp)\n    l1 = ratio * advantages\n    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages\n    m = torch.min(l1, l2)\n    masked = (m * mask).sum() / mask.sum()\n    return -masked\n\n\ndef value_loss(values, old_values, returns, clip):\n    vclip = old_values + torch.clamp(values - old_values, -clip, clip)\n    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()\n    return loss\n\n\ndef reverse_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return torch.exp(-d) - 1.0 + d\n\n\ndef symmetric_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0\n\n\ndef importance_ratio(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    if clip is not None:\n        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)\n    return ratio\n\n\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):\n    return beta * (chosen_reward - rejected_reward)\n\n\ndef huber_value_loss(values, returns, delta):\n    return F.huber_loss(values, returns, delta=delta)\n\n\ndef clip_fraction(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)\n    return clipped.float().mean()\n```\n\n### Per-function results (all PASS)\n| Function | Result | Key findings |\n|---|---|---|\n| `dpo_loss` | PASS 300/300 | Mean over batch → scalar; sign `-(1-ls)·logσ(logits) - ls·logσ(-logits)` |\n| `ipo_loss` | PASS 300/300 | `((pc-rc)-(pr-rr) - 1/(2β))²`, mean → scalar |\n| `kl_penalty` | PASS 400/400 | Per-element (no reduction); `d=logp-ref`; k1=d, k2=0.5d², k3=exp(-d)-1+d; unknown estimator → `ValueError` |\n| `clipped_pg_loss` | PASS 300/300 | `clip_low/clip_high` are epsilons (bounds `1-cl`..`1+ch`); `-masked_mean(min(l1,l2))` → scalar |\n| `value_loss` | PASS 300/300 | `0.5·mean(max((v-ret)²,(vclip-ret)²))`, 0.5 factor present |\n| `reverse_kl` | PASS 300/300 | Per-element k3 form: `exp(-d)-1+d`, d=logp-ref |\n| `symmetric_kl` | PASS 300/300 | Per-element `0.5·(exp(d)+exp(-d))-1` = ½(reverse+forward k3) |\n| `importance_ratio` | PASS 300/300 | `exp(logp-old)`, clamp to `[1-clip,1+clip]` only if clip not None |\n| `bradley_terry_logit` | PASS 300/300 | Just the logit `β·(cr-rr)`, per-element (no logsigmoid) |\n| `huber_value_loss` | PASS 400/400 | `F.huber_loss` (delta·(|x|-0.5delta) form), **not** smooth_l1 , no extra 0.5 |\n| `clip_fraction` | PASS 400/400 | `mean((ratio > 1+clip) \\| (ratio < 1-clip))` , NOT `\\|ratio-1\\|>clip` (differs at float boundary) |\n\nThe most subtle finding: `clip_fraction` uses separate `>`/`<` bound comparisons rather than `abs(ratio-1) > clip`; these diverge at float32 boundaries (e.g. `1+0.2` rounds to `1.20000004768`, so a ratio equal to it is not counted). I verified this with crafted boundary inputs.\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: aea930bae11f8f34f (use SendMessage with to: 'aea930bae11f8f34f', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29879\ntool_uses: 15\nduration_ms: 151628</usage>"}

{"type": "text", "text": "All 7 functions implemented and verified. `/app/part4.py` is standalone (only `import torch`, no reforacle).\n\n## Key findings from probing\n\n- **Time axis is dim 0** (first dim) for `gae`/`discounted_returns`/`lambda_returns`, not the last dim. For 2D input shape is `(T, B)`; recursion runs backward over dim 0. `next_value` is a scalar or `(B,)` tensor used as the bootstrap `V_{T}` for the final step. `values[t]` becomes the next-value as we recurse backward.\n- **grpo_advantages**: contiguous groups of `group_size` along the flattened rewards; std is **biased** (`unbiased=False`); `eps = 1e-6` applied **outside** the sqrt (`adv/(std+1e-6)`); output is **flattened to 1D** regardless of input shape.\n- **rloo_advantages**: factor is exactly `n/(n-1)` times `(r - group_mean)`; output flattened to 1D.\n- **group_mean_baseline**: `r - group_mean`, no std; output flattened to 1D.\n- **advantage_mean_std**: returns a **stacked tensor `[mean, std]`** (order mean, std). It is **mask-weighted** (mask used as weights, not boolean): `mean = Σ(w·x)/Σw`, `std = sqrt(Σ(w·(x-mean)²)/Σw)` (**biased**, divide by `Σw`). Empty mask → `[0, 0]` (via nan handling); single element → `[x, 0]`.\n\n## Per-function results (compare n≥300 each, atol=1e-6/rtol=1e-5)\n\n| Function | Cases tested | Result |\n|---|---|---|\n| grpo_advantages | no-std, std, 2D, small-std, gs=1 | PASS |\n| gae | 1D & 2D × 5 (gamma,lam) combos incl. edge 0.0/1.0 | PASS |\n| discounted_returns | 1D & 2D × gamma∈{0.9,0.99,1.0,0.0} | PASS |\n| lambda_returns | 1D & 2D × 3 combos | PASS |\n| rloo_advantages | gs=3 1D, gs=5 2D | PASS |\n| group_mean_baseline | gs=4 1D, gs=3 2D | PASS |\n| advantage_mean_std | bool/frac/2D masks, empty, single-elem | PASS |\n\nAll 39 test configurations passed (100%). Full source of `/app/part4.py`:\n\n```python\nimport torch\n\n\ndef grpo_advantages(rewards, group_size, scale_by_std):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = groups - mean\n    if scale_by_std:\n        std = groups.std(dim=1, unbiased=False, keepdim=True)\n        adv = adv / (std + 1e-6)\n    return adv.reshape(-1)\n\n\ndef gae(rewards, values, next_value, gamma, lam):\n    T = rewards.shape[0]\n    advantages = torch.zeros_like(rewards)\n    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    next_v = next_value\n    for t in range(T - 1, -1, -1):\n        delta = rewards[t] + gamma * next_v - values[t]\n        last_adv = delta + gamma * lam * last_adv\n        advantages[t] = last_adv\n        next_v = values[t]\n    return advantages\n\n\ndef discounted_returns(rewards, gamma):\n    T = rewards.shape[0]\n    returns = torch.zeros_like(rewards)\n    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    for t in range(T - 1, -1, -1):\n        acc = rewards[t] + gamma * acc\n        returns[t] = acc\n    return returns\n\n\ndef lambda_returns(rewards, values, next_value, gamma, lam):\n    return gae(rewards, values, next_value, gamma, lam) + values\n\n\ndef rloo_advantages(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = (group_size / (group_size - 1)) * (groups - mean)\n    return adv.reshape(-1)\n\n\ndef group_mean_baseline(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    return (groups - mean).reshape(-1)\n\n\ndef advantage_mean_std(advantages, mask):\n    w = mask\n    wsum = w.sum()\n    mean = (w * advantages).sum() / wsum\n    var = (w * (advantages - mean) ** 2).sum() / wsum\n    std = torch.sqrt(var)\n    result = torch.stack([mean, std])\n    result = torch.nan_to_num(result, nan=0.0)\n    return result\n```\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: afc0516e74454f57b (use SendMessage with to: 'afc0516e74454f57b', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29811\ntool_uses: 22\nduration_ms: 184062</usage>"}

{"type": "text", "text": "All done. Here is the final state.\n\n## Summary\n\nAll 10 functions implemented in pure torch in `/app/part1.py` (standalone, no reforacle import) and verified with `compare()` at n≥300 across multiple shapes plus edge cases (empty/all-zero masks, single elements, negatives, vocab=1).\n\nPass/fail per function (all over many shapes + edge cases):\n- masked_mean: PASS\n- masked_sum: PASS\n- logsumexp: PASS\n- log_softmax: PASS\n- entropy: PASS\n- normalize: PASS\n- whiten: PASS\n- masked_whiten: PASS\n- masked_max: PASS\n- normalized_entropy: PASS\n\nKey conventions discovered:\n- `masked_mean` axis=None: 0.0 fallback on empty mask; axis=int uses `denom.clamp(min=1)` (0/1=0, no keepdim).\n- `masked_sum`: plain `(v*m).sum(dim=axis)`, no special empty handling.\n- `entropy` = masked_mean of per-position softmax entropy over last dim; returns scalar; 0.0 on all-zero mask.\n- `normalized_entropy` = entropy / log(vocab_size) where vocab = last dim; nan when vocab=1 (matches ref).\n- `normalize` = `(x-mean)/(std+eps)` with **unbiased** std.\n- `whiten`: uses **masked** mean and **biased** masked variance, `(v-mean)/sqrt(var+1e-8)`; when `shift_mean=False` adds mean back; denominator clamped to min=1 for empty mask (gives finite values, not nan).\n- `masked_whiten`: same as whiten but multiplies the whitened result by mask **before** the optional mean shift-back , so empty mask yields all zeros.\n- `masked_max`: global max over masked positions (fill unmasked with -inf); special-cases empty mask to 0.0.\n\nFull source of `/app/part1.py`:\n\n```python\nfrom __future__ import annotations\n\nimport math\n\nimport torch\n\n\ndef masked_mean(values, mask, axis=None):\n    if axis is None:\n        denom = mask.sum()\n        if denom == 0:\n            return torch.zeros((), dtype=values.dtype, device=values.device)\n        return (values * mask).sum() / denom\n    num = (values * mask).sum(dim=axis)\n    denom = mask.sum(dim=axis)\n    return num / denom.clamp(min=1)\n\n\ndef masked_sum(values, mask, axis=None):\n    if axis is None:\n        return (values * mask).sum()\n    return (values * mask).sum(dim=axis)\n\n\ndef logsumexp(x, axis):\n    return torch.logsumexp(x, dim=axis)\n\n\ndef log_softmax(x, axis):\n    return torch.log_softmax(x, dim=axis)\n\n\ndef entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom\n\n\ndef normalize(x, eps):\n    return (x - x.mean()) / (x.std() + eps)\n\n\ndef whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    out = out * mask\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_max(values, mask):\n    if mask.sum() == 0:\n        return torch.zeros((), dtype=values.dtype, device=values.device)\n    filled = values.masked_fill(mask == 0, float(\"-inf\"))\n    return filled.max()\n\n\ndef normalized_entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    vocab = logits.shape[-1]\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom / math.log(vocab)\n```"}

{"type": "text", "text": "agentId: a8ab0e0c2a3fc9eb3 (use SendMessage with to: 'a8ab0e0c2a3fc9eb3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 37980\ntool_uses: 33\nduration_ms: 262016</usage>"}

{"type": "text", "text": "All 10 functions reverse-engineered and verified. Here is the final report.\n\n## Summary\n\nI reverse-engineered all 10 `reforacle` functions by probing with varied shapes, dtypes, signs, and edge cases, then verified each against the oracle with `compare()` at n≥300 (plus larger stress runs).\n\n### Per-function pass/fail (all PASS)\n```\ncumulative_max ...... PASS  (1D, 2D, int, single-elem)\nquantile_lower ...... PASS  (1D, 2D, q=0/1, single-row/col)\nmedian_reward ....... PASS  (1D, 2D, single)\nmode_label .......... PASS  (1D, 2D, ties, all-same, single)\nargmax_tokens ....... PASS  (1D, 2D, single-elem last dim)\nfirst_nonzero_index . PASS  (binary/frac/int/count masks, 1D+2D, all-zero)\npad_mask_from_lengths PASS  (normal, len>max_len, zeros)\nbucketize_reward .... PASS  (random, exact boundaries, empty boundaries)\ntop_k_mask .......... PASS  (1D, 2D, k>n, ties, k=0 raises)\ntop_p_mask .......... PASS  (1D, 2D, straddle, peaky, uniform)\n```\n\n### Key conventions discovered (the non-obvious ones)\n- **cumulative_max**: NOT a normal cummax. It is an *exclusive/shifted* cummax along dim 0: `out[0]=x[0]`, `out[i]=max(x[0..i-1])`. Returns values only (no tuple).\n- **quantile_lower / median_reward (2D)**: operate along dim 0 but in a peculiar way , they **sort each row**, then median/quantile is taken over rows *by original row index*. median = average of `sort(row[(n-1)//2])` and `sort(row[n//2])`; quantile_lower = `sort(row[floor(q*(n-1))])`. (1D uses plain `torch.quantile` with `interpolation='lower'`/`'linear'`.)\n- **mode_label**: most frequent label, ties broken to the **larger** value (opposite of `torch.mode`); per-row for 2D; scalar int64.\n- **first_nonzero_index**: implemented as the buggy idiom `argmax(mask.long() * arange(n,0,-1))` with a `sum(mask) <= 0 → -1` guard. For a true 0/1 mask this equals first-nonzero, but values are truncated-to-long and position-weighted, so it's only equivalent for proper masks. Per-row for 2D, -1 if a row sums to ≤0.\n- **bucketize_reward**: `torch.bucketize(..., right=True)`.\n- **top_k_mask**: returns a **bool** mask via threshold `logits >= kth-largest-value` (so ties can select >k elements); `k` clamped to `min(k, n)` (k>n → all True); `k=0` raises RuntimeError.\n- **top_p_mask**: returns **renormalized probabilities** (kept elements sum to 1, excluded set to 0), NOT a mask. Inclusion rule uses the *exclusive* cumsum of descending-sorted probs: keep where `cumsum_before_token < p`, always keeping the top-1.\n\nDeliverable written to `/app/part2.py` (standalone, imports only `torch`; the only \"reforacle\" mention is in a comment). Full source is shown above. `/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: ab8a55331340147b3 (use SendMessage with to: 'ab8a55331340147b3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 138643\ntool_uses: 112\nduration_ms: 1361957</usage>"}
Agent
{
  "description": "Reverse-engineer loss/KL primitives",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`). Reproduce exact numerical behavior in pure torch. CANNOT read source; only call & compare.\n\nHelper: `from harness import compare` (/app/harness.py) , `compare(ref_fn, cand_fn, make_inputs, n=300)`, atol=1e-6, rtol=1e-5. Use heavily.\n\nImplement these 11 functions EXACTLY. Probe varied shapes/values/edge cases.\n\nSignatures (keep EXACTLY):\n```\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):   # DPO. pc,pr=policy chosen/rejected logprobs; rc,rr=reference chosen/rejected logprobs. logits = beta*((pc-rc)-(pr-rr)); loss = -(1-ls)*logsigmoid(logits) - ls*logsigmoid(-logits); reduction MEAN over batch? PROBE. Determine sign & reduction & scalar output.\ndef ipo_loss(pc, pr, rc, rr, beta):                    # IPO: loss = ((pc-rc)-(pr-rr) - 1/(2*beta))^2, mean. PROBE exact form.\ndef kl_penalty(logp, ref_logp, estimator):             # estimator is a string: 'k1'=(logp-ref_logp)? or (ref-logp)? 'k2'=0.5*diff^2, 'k3'=exp(-d)-1+d ... PROBE each estimator string and sign. Determine which arg order.\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):  # PPO policy loss. ratio=exp(logp-old_logp); l1=ratio*adv; l2=clamp(ratio,1-clip_low,1+clip_high)*adv; loss = -masked_mean(min(l1,l2), mask). PROBE clip param meaning (are clip_low/clip_high the epsilons, so bounds 1-clip_low..1+clip_high?) and reduction. sign.\ndef value_loss(values, old_values, returns, clip):     # clipped value loss: vpred=values; vclip=old+clamp(values-old,-clip,clip); loss=0.5*mean(max((vpred-returns)^2,(vclip-returns)^2)). PROBE 0.5 factor & max & reduction.\ndef reverse_kl(logp, ref_logp):                        # scalar? per-elem? reverse KL estimate. PROBE sign/order & reduction.\ndef symmetric_kl(logp, ref_logp):                      # PROBE\ndef importance_ratio(logp, old_logp, clip):            # exp(logp-old_logp), then clamp to [1-clip,1+clip] or [.., ]? clip may be None. PROBE whether clip applied and bounds.\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):  # PROBE: beta*(chosen-rejected)? returns logsigmoid? or just the logit? likely returns beta*(cr-rr). Or -logsigmoid(...) loss. PROBE output.\ndef huber_value_loss(values, returns, delta):          # Huber/smooth L1 between values and returns with delta. reduction mean. PROBE (smooth_l1 uses 0.5x^2 for |x|<delta else delta*(|x|-0.5delta)). Determine if extra 0.5.\ndef clip_fraction(logp, old_logp, clip):               # fraction of ratios that got clipped: mean( |ratio-1| > clip ). PROBE exact condition.\n```\n\nNail by probing:\n- reduction (mean over batch -> scalar) for dpo/ipo/losses. Print reforacle output to see if scalar.\n- kl_penalty: try estimator in {'k1','k2','k3','mse','abs',...}. Determine arg order (logp-ref vs ref-logp). k1 typically = logp - ref_logp (or negative). k3 = (ref_logp-logp).exp() - (ref_logp-logp) - 1 >=0. Test which matches.\n- clipped_pg_loss: determine whether clip_low,clip_high are epsilons added/subtracted from 1. Whether reduction is masked_mean(min(...)) with negative sign.\n- importance_ratio clip: test clip=None and clip=0.2.\n- bradley_terry_logit: print output for known inputs to infer formula.\n- reverse_kl/symmetric_kl: reverse_kl of policy vs ref. Given only logp and ref_logp (per-sample logprobs), these are likely simple estimators: reverse_kl = mean(exp(ref_logp-logp)*(ref_logp-logp))? or mean(logp-ref_logp)? PROBE by comparing to candidates. symmetric_kl likely reverse+forward.\n\nDeliverables:\n1. Write /app/part5.py: `import torch` + 11 pure-torch defs (NO reforacle import). torch.nn.functional as F allowed.\n2. Verify each compare() n>=300 across shapes/edge cases; iterate to robust pass. Test estimator strings, clip=None, label_smoothing=0 and >0.\n3. Final message: FULL /app/part5.py source + per-function pass/fail.\n\nDo not modify /app/objectives.py.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 6 functions pass across shapes and edge cases. Done.\n\n## Summary\n\nReverse-engineered all 6 functions and wrote `/app/part3.py` (pure torch, no reforacle import). Verified each with `compare()` at n≥300 across (B,T,V) and (N,V) shapes plus edge cases.\n\n**Per-function results (all PASS):**\n\n| Function | Behavior discovered | Result |\n|---|---|---|\n| `token_logprobs` | `log_softmax(-1).gather(labels)` → shape = labels.shape | PASS 300/300 |\n| `selective_logprobs` | token logprobs × mask, then **sum over seq** → shape (B,) | PASS 300/300 |\n| `sequence_logprob` | sum of (logprob×mask) over seq; if `length_normalize` truthy, divide by `mask.sum(-1).clamp(min=1)` (empty mask → 0, not nan) | PASS (both flags + empty-mask) |\n| `smoothed_nll` | `(1-s)*nll + s*(-mean_v logp)` per token, reduced by **mean over all** → scalar | PASS 300/300 |\n| `cross_entropy` | log_softmax, gather on `labels.clamp(min=0)` (so `-100` is safe but an in-range out-of-vocab ignore_index still raises), mask by `labels!=ignore_index`, `sum/mask.sum().clamp(min=1)` → **all-ignored gives 0, not nan** (differs from `F.cross_entropy`). Works for 2D (N,V) and 3D (B,T,V) | PASS 300/300 + all-ignored |\n| `logprob_at_temperature` | `log_softmax(logits/temperature,-1).gather(labels)` | PASS 300/300 |\n\n**Key non-obvious findings:**\n- `selective_logprobs` is a *reduced* value (sum over sequence), shape (B,), not element-wise like `token_logprobs`.\n- `sequence_logprob` normalizes with a `clamp(min=1)` denominator, so empty masks yield 0 rather than nan.\n- `cross_entropy` does **not** wrap `F.cross_entropy`: it clamps negatives before gather and uses a `clamp(min=1)` denominator, giving **0 for the all-ignored case** where `F.cross_entropy` returns nan.\n\nFull source is at `/app/part3.py`."}

{"type": "text", "text": "agentId: a579217cf7f7f4bf4 (use SendMessage with to: 'a579217cf7f7f4bf4', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 23434\ntool_uses: 16\nduration_ms: 150042</usage>"}

{"type": "text", "text": "All edge cases pass across 2D/3D shapes, extreme values, boundary conditions, clip=None, all-mask, and varied label_smoothing/delta/clip values.\n\n## Summary\n\nI reverse-engineered all 11 `reforacle` functions by probing and verified each with `compare()` at n≥300 (many at 400-500), plus extensive edge-case runs. **All 11 functions PASS.**\n\n### Deliverable: `/app/part5.py`\n\n```python\nfrom __future__ import annotations\n\nimport torch\nimport torch.nn.functional as F\n\n\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):\n    logits = beta * ((pc - rc) - (pr - rr))\n    ls = label_smoothing\n    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)\n    return loss.mean()\n\n\ndef ipo_loss(pc, pr, rc, rr, beta):\n    logits = (pc - rc) - (pr - rr)\n    loss = (logits - 1.0 / (2.0 * beta)) ** 2\n    return loss.mean()\n\n\ndef kl_penalty(logp, ref_logp, estimator):\n    d = logp - ref_logp\n    if estimator == \"k1\":\n        return d\n    if estimator == \"k2\":\n        return 0.5 * d * d\n    if estimator == \"k3\":\n        return torch.exp(-d) - 1.0 + d\n    raise ValueError(estimator)\n\n\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):\n    ratio = torch.exp(logp - old_logp)\n    l1 = ratio * advantages\n    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages\n    m = torch.min(l1, l2)\n    masked = (m * mask).sum() / mask.sum()\n    return -masked\n\n\ndef value_loss(values, old_values, returns, clip):\n    vclip = old_values + torch.clamp(values - old_values, -clip, clip)\n    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()\n    return loss\n\n\ndef reverse_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return torch.exp(-d) - 1.0 + d\n\n\ndef symmetric_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0\n\n\ndef importance_ratio(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    if clip is not None:\n        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)\n    return ratio\n\n\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):\n    return beta * (chosen_reward - rejected_reward)\n\n\ndef huber_value_loss(values, returns, delta):\n    return F.huber_loss(values, returns, delta=delta)\n\n\ndef clip_fraction(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)\n    return clipped.float().mean()\n```\n\n### Per-function results (all PASS)\n| Function | Result | Key findings |\n|---|---|---|\n| `dpo_loss` | PASS 300/300 | Mean over batch → scalar; sign `-(1-ls)·logσ(logits) - ls·logσ(-logits)` |\n| `ipo_loss` | PASS 300/300 | `((pc-rc)-(pr-rr) - 1/(2β))²`, mean → scalar |\n| `kl_penalty` | PASS 400/400 | Per-element (no reduction); `d=logp-ref`; k1=d, k2=0.5d², k3=exp(-d)-1+d; unknown estimator → `ValueError` |\n| `clipped_pg_loss` | PASS 300/300 | `clip_low/clip_high` are epsilons (bounds `1-cl`..`1+ch`); `-masked_mean(min(l1,l2))` → scalar |\n| `value_loss` | PASS 300/300 | `0.5·mean(max((v-ret)²,(vclip-ret)²))`, 0.5 factor present |\n| `reverse_kl` | PASS 300/300 | Per-element k3 form: `exp(-d)-1+d`, d=logp-ref |\n| `symmetric_kl` | PASS 300/300 | Per-element `0.5·(exp(d)+exp(-d))-1` = ½(reverse+forward k3) |\n| `importance_ratio` | PASS 300/300 | `exp(logp-old)`, clamp to `[1-clip,1+clip]` only if clip not None |\n| `bradley_terry_logit` | PASS 300/300 | Just the logit `β·(cr-rr)`, per-element (no logsigmoid) |\n| `huber_value_loss` | PASS 400/400 | `F.huber_loss` (delta·(|x|-0.5delta) form), **not** smooth_l1 , no extra 0.5 |\n| `clip_fraction` | PASS 400/400 | `mean((ratio > 1+clip) \\| (ratio < 1-clip))` , NOT `\\|ratio-1\\|>clip` (differs at float boundary) |\n\nThe most subtle finding: `clip_fraction` uses separate `>`/`<` bound comparisons rather than `abs(ratio-1) > clip`; these diverge at float32 boundaries (e.g. `1+0.2` rounds to `1.20000004768`, so a ratio equal to it is not counted). I verified this with crafted boundary inputs.\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: aea930bae11f8f34f (use SendMessage with to: 'aea930bae11f8f34f', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29879\ntool_uses: 15\nduration_ms: 151628</usage>"}

{"type": "text", "text": "All 7 functions implemented and verified. `/app/part4.py` is standalone (only `import torch`, no reforacle).\n\n## Key findings from probing\n\n- **Time axis is dim 0** (first dim) for `gae`/`discounted_returns`/`lambda_returns`, not the last dim. For 2D input shape is `(T, B)`; recursion runs backward over dim 0. `next_value` is a scalar or `(B,)` tensor used as the bootstrap `V_{T}` for the final step. `values[t]` becomes the next-value as we recurse backward.\n- **grpo_advantages**: contiguous groups of `group_size` along the flattened rewards; std is **biased** (`unbiased=False`); `eps = 1e-6` applied **outside** the sqrt (`adv/(std+1e-6)`); output is **flattened to 1D** regardless of input shape.\n- **rloo_advantages**: factor is exactly `n/(n-1)` times `(r - group_mean)`; output flattened to 1D.\n- **group_mean_baseline**: `r - group_mean`, no std; output flattened to 1D.\n- **advantage_mean_std**: returns a **stacked tensor `[mean, std]`** (order mean, std). It is **mask-weighted** (mask used as weights, not boolean): `mean = Σ(w·x)/Σw`, `std = sqrt(Σ(w·(x-mean)²)/Σw)` (**biased**, divide by `Σw`). Empty mask → `[0, 0]` (via nan handling); single element → `[x, 0]`.\n\n## Per-function results (compare n≥300 each, atol=1e-6/rtol=1e-5)\n\n| Function | Cases tested | Result |\n|---|---|---|\n| grpo_advantages | no-std, std, 2D, small-std, gs=1 | PASS |\n| gae | 1D & 2D × 5 (gamma,lam) combos incl. edge 0.0/1.0 | PASS |\n| discounted_returns | 1D & 2D × gamma∈{0.9,0.99,1.0,0.0} | PASS |\n| lambda_returns | 1D & 2D × 3 combos | PASS |\n| rloo_advantages | gs=3 1D, gs=5 2D | PASS |\n| group_mean_baseline | gs=4 1D, gs=3 2D | PASS |\n| advantage_mean_std | bool/frac/2D masks, empty, single-elem | PASS |\n\nAll 39 test configurations passed (100%). Full source of `/app/part4.py`:\n\n```python\nimport torch\n\n\ndef grpo_advantages(rewards, group_size, scale_by_std):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = groups - mean\n    if scale_by_std:\n        std = groups.std(dim=1, unbiased=False, keepdim=True)\n        adv = adv / (std + 1e-6)\n    return adv.reshape(-1)\n\n\ndef gae(rewards, values, next_value, gamma, lam):\n    T = rewards.shape[0]\n    advantages = torch.zeros_like(rewards)\n    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    next_v = next_value\n    for t in range(T - 1, -1, -1):\n        delta = rewards[t] + gamma * next_v - values[t]\n        last_adv = delta + gamma * lam * last_adv\n        advantages[t] = last_adv\n        next_v = values[t]\n    return advantages\n\n\ndef discounted_returns(rewards, gamma):\n    T = rewards.shape[0]\n    returns = torch.zeros_like(rewards)\n    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    for t in range(T - 1, -1, -1):\n        acc = rewards[t] + gamma * acc\n        returns[t] = acc\n    return returns\n\n\ndef lambda_returns(rewards, values, next_value, gamma, lam):\n    return gae(rewards, values, next_value, gamma, lam) + values\n\n\ndef rloo_advantages(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = (group_size / (group_size - 1)) * (groups - mean)\n    return adv.reshape(-1)\n\n\ndef group_mean_baseline(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    return (groups - mean).reshape(-1)\n\n\ndef advantage_mean_std(advantages, mask):\n    w = mask\n    wsum = w.sum()\n    mean = (w * advantages).sum() / wsum\n    var = (w * (advantages - mean) ** 2).sum() / wsum\n    std = torch.sqrt(var)\n    result = torch.stack([mean, std])\n    result = torch.nan_to_num(result, nan=0.0)\n    return result\n```\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: afc0516e74454f57b (use SendMessage with to: 'afc0516e74454f57b', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29811\ntool_uses: 22\nduration_ms: 184062</usage>"}

{"type": "text", "text": "All done. Here is the final state.\n\n## Summary\n\nAll 10 functions implemented in pure torch in `/app/part1.py` (standalone, no reforacle import) and verified with `compare()` at n≥300 across multiple shapes plus edge cases (empty/all-zero masks, single elements, negatives, vocab=1).\n\nPass/fail per function (all over many shapes + edge cases):\n- masked_mean: PASS\n- masked_sum: PASS\n- logsumexp: PASS\n- log_softmax: PASS\n- entropy: PASS\n- normalize: PASS\n- whiten: PASS\n- masked_whiten: PASS\n- masked_max: PASS\n- normalized_entropy: PASS\n\nKey conventions discovered:\n- `masked_mean` axis=None: 0.0 fallback on empty mask; axis=int uses `denom.clamp(min=1)` (0/1=0, no keepdim).\n- `masked_sum`: plain `(v*m).sum(dim=axis)`, no special empty handling.\n- `entropy` = masked_mean of per-position softmax entropy over last dim; returns scalar; 0.0 on all-zero mask.\n- `normalized_entropy` = entropy / log(vocab_size) where vocab = last dim; nan when vocab=1 (matches ref).\n- `normalize` = `(x-mean)/(std+eps)` with **unbiased** std.\n- `whiten`: uses **masked** mean and **biased** masked variance, `(v-mean)/sqrt(var+1e-8)`; when `shift_mean=False` adds mean back; denominator clamped to min=1 for empty mask (gives finite values, not nan).\n- `masked_whiten`: same as whiten but multiplies the whitened result by mask **before** the optional mean shift-back , so empty mask yields all zeros.\n- `masked_max`: global max over masked positions (fill unmasked with -inf); special-cases empty mask to 0.0.\n\nFull source of `/app/part1.py`:\n\n```python\nfrom __future__ import annotations\n\nimport math\n\nimport torch\n\n\ndef masked_mean(values, mask, axis=None):\n    if axis is None:\n        denom = mask.sum()\n        if denom == 0:\n            return torch.zeros((), dtype=values.dtype, device=values.device)\n        return (values * mask).sum() / denom\n    num = (values * mask).sum(dim=axis)\n    denom = mask.sum(dim=axis)\n    return num / denom.clamp(min=1)\n\n\ndef masked_sum(values, mask, axis=None):\n    if axis is None:\n        return (values * mask).sum()\n    return (values * mask).sum(dim=axis)\n\n\ndef logsumexp(x, axis):\n    return torch.logsumexp(x, dim=axis)\n\n\ndef log_softmax(x, axis):\n    return torch.log_softmax(x, dim=axis)\n\n\ndef entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom\n\n\ndef normalize(x, eps):\n    return (x - x.mean()) / (x.std() + eps)\n\n\ndef whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    out = out * mask\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_max(values, mask):\n    if mask.sum() == 0:\n        return torch.zeros((), dtype=values.dtype, device=values.device)\n    filled = values.masked_fill(mask == 0, float(\"-inf\"))\n    return filled.max()\n\n\ndef normalized_entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    vocab = logits.shape[-1]\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom / math.log(vocab)\n```"}

{"type": "text", "text": "agentId: a8ab0e0c2a3fc9eb3 (use SendMessage with to: 'a8ab0e0c2a3fc9eb3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 37980\ntool_uses: 33\nduration_ms: 262016</usage>"}

{"type": "text", "text": "All 10 functions reverse-engineered and verified. Here is the final report.\n\n## Summary\n\nI reverse-engineered all 10 `reforacle` functions by probing with varied shapes, dtypes, signs, and edge cases, then verified each against the oracle with `compare()` at n≥300 (plus larger stress runs).\n\n### Per-function pass/fail (all PASS)\n```\ncumulative_max ...... PASS  (1D, 2D, int, single-elem)\nquantile_lower ...... PASS  (1D, 2D, q=0/1, single-row/col)\nmedian_reward ....... PASS  (1D, 2D, single)\nmode_label .......... PASS  (1D, 2D, ties, all-same, single)\nargmax_tokens ....... PASS  (1D, 2D, single-elem last dim)\nfirst_nonzero_index . PASS  (binary/frac/int/count masks, 1D+2D, all-zero)\npad_mask_from_lengths PASS  (normal, len>max_len, zeros)\nbucketize_reward .... PASS  (random, exact boundaries, empty boundaries)\ntop_k_mask .......... PASS  (1D, 2D, k>n, ties, k=0 raises)\ntop_p_mask .......... PASS  (1D, 2D, straddle, peaky, uniform)\n```\n\n### Key conventions discovered (the non-obvious ones)\n- **cumulative_max**: NOT a normal cummax. It is an *exclusive/shifted* cummax along dim 0: `out[0]=x[0]`, `out[i]=max(x[0..i-1])`. Returns values only (no tuple).\n- **quantile_lower / median_reward (2D)**: operate along dim 0 but in a peculiar way , they **sort each row**, then median/quantile is taken over rows *by original row index*. median = average of `sort(row[(n-1)//2])` and `sort(row[n//2])`; quantile_lower = `sort(row[floor(q*(n-1))])`. (1D uses plain `torch.quantile` with `interpolation='lower'`/`'linear'`.)\n- **mode_label**: most frequent label, ties broken to the **larger** value (opposite of `torch.mode`); per-row for 2D; scalar int64.\n- **first_nonzero_index**: implemented as the buggy idiom `argmax(mask.long() * arange(n,0,-1))` with a `sum(mask) <= 0 → -1` guard. For a true 0/1 mask this equals first-nonzero, but values are truncated-to-long and position-weighted, so it's only equivalent for proper masks. Per-row for 2D, -1 if a row sums to ≤0.\n- **bucketize_reward**: `torch.bucketize(..., right=True)`.\n- **top_k_mask**: returns a **bool** mask via threshold `logits >= kth-largest-value` (so ties can select >k elements); `k` clamped to `min(k, n)` (k>n → all True); `k=0` raises RuntimeError.\n- **top_p_mask**: returns **renormalized probabilities** (kept elements sum to 1, excluded set to 0), NOT a mask. Inclusion rule uses the *exclusive* cumsum of descending-sorted probs: keep where `cumsum_before_token < p`, always keeping the top-1.\n\nDeliverable written to `/app/part2.py` (standalone, imports only `torch`; the only \"reforacle\" mention is in a comment). Full source is shown above. `/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: ab8a55331340147b3 (use SendMessage with to: 'ab8a55331340147b3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 138643\ntool_uses: 112\nduration_ms: 1361957</usage>"}
Agent
{
  "description": "Reverse-engineer advantage/return functions",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`) to reproduce its exact numerical behavior in pure `torch`. CANNOT read source; only call & compare.\n\nHelper: `from harness import compare` (/app/harness.py) , `compare(ref_fn, cand_fn, make_inputs, n=300)`, match at atol=1e-6, rtol=1e-5. Use heavily.\n\nImplement these 7 functions EXACTLY. Probe with varied shapes/values/edge cases.\n\nSignatures (keep EXACTLY):\n```\ndef grpo_advantages(rewards, group_size, scale_by_std):   # reshape rewards into groups of group_size; advantage = reward - group_mean; if scale_by_std divide by (group_std + eps). Determine eps and biased/unbiased std, and output shape (flattened back). PROBE.\ndef gae(rewards, values, next_value, gamma, lam):         # generalized advantage estimation. rewards/values shape (T,) or (B,T)? next_value scalar/(B,)? deltas_t = r_t + gamma*V_{t+1} - V_t; A_t = delta + gamma*lam*A_{t+1}. Return advantages only. PROBE shape/orientation (which axis is time).\ndef discounted_returns(rewards, gamma):                   # G_t = r_t + gamma*G_{t+1}. PROBE time axis.\ndef lambda_returns(rewards, values, next_value, gamma, lam): # returns = advantages + values (TD-lambda). PROBE vs gae.\ndef rloo_advantages(rewards, group_size):                 # leave-one-out: adv_i = r_i - mean_{j!=i} r_j = (n/(n-1))*(r_i - groupmean). PROBE exact factor.\ndef group_mean_baseline(rewards, group_size):             # r - group_mean (no std). PROBE output shape.\ndef advantage_mean_std(advantages, mask):                 # return (mean, std) over masked entries. std biased/unbiased? tuple order? PROBE.\n```\n\nCritical to determine by probing:\n- Time axis for gae/discounted_returns/lambda_returns: test with 1D (T,) and 2D. Figure out whether recursion runs along last dim. next_value: shape and role (bootstrap for final step).\n- grpo_advantages: how rewards are grouped (contiguous groups of size group_size along dim 0). std: unbiased or biased? eps value (try 1e-8, 1e-6, 1e-4, and inside/outside sqrt). scale_by_std is a bool. Check output shape equals input shape.\n- rloo: verify factor n/(n-1) vs plain.\n- advantage_mean_std: returns a tuple (mean, std). Determine std convention (unbiased?) and masked (only where mask=1). Empty-mask behavior.\n- gamma/lam are floats.\n\nDeliverables:\n1. Write /app/part4.py: `import torch` + 7 pure-torch defs (NO reforacle import), standalone.\n2. Verify each compare() n>=300 across shapes/edge cases; iterate to robust pass. For gae/returns test multiple gamma,lam and both 1D/2D.\n3. Final message: FULL /app/part4.py source + per-function pass/fail.\n\nDo not modify /app/objectives.py.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 6 functions pass across shapes and edge cases. Done.\n\n## Summary\n\nReverse-engineered all 6 functions and wrote `/app/part3.py` (pure torch, no reforacle import). Verified each with `compare()` at n≥300 across (B,T,V) and (N,V) shapes plus edge cases.\n\n**Per-function results (all PASS):**\n\n| Function | Behavior discovered | Result |\n|---|---|---|\n| `token_logprobs` | `log_softmax(-1).gather(labels)` → shape = labels.shape | PASS 300/300 |\n| `selective_logprobs` | token logprobs × mask, then **sum over seq** → shape (B,) | PASS 300/300 |\n| `sequence_logprob` | sum of (logprob×mask) over seq; if `length_normalize` truthy, divide by `mask.sum(-1).clamp(min=1)` (empty mask → 0, not nan) | PASS (both flags + empty-mask) |\n| `smoothed_nll` | `(1-s)*nll + s*(-mean_v logp)` per token, reduced by **mean over all** → scalar | PASS 300/300 |\n| `cross_entropy` | log_softmax, gather on `labels.clamp(min=0)` (so `-100` is safe but an in-range out-of-vocab ignore_index still raises), mask by `labels!=ignore_index`, `sum/mask.sum().clamp(min=1)` → **all-ignored gives 0, not nan** (differs from `F.cross_entropy`). Works for 2D (N,V) and 3D (B,T,V) | PASS 300/300 + all-ignored |\n| `logprob_at_temperature` | `log_softmax(logits/temperature,-1).gather(labels)` | PASS 300/300 |\n\n**Key non-obvious findings:**\n- `selective_logprobs` is a *reduced* value (sum over sequence), shape (B,), not element-wise like `token_logprobs`.\n- `sequence_logprob` normalizes with a `clamp(min=1)` denominator, so empty masks yield 0 rather than nan.\n- `cross_entropy` does **not** wrap `F.cross_entropy`: it clamps negatives before gather and uses a `clamp(min=1)` denominator, giving **0 for the all-ignored case** where `F.cross_entropy` returns nan.\n\nFull source is at `/app/part3.py`."}

{"type": "text", "text": "agentId: a579217cf7f7f4bf4 (use SendMessage with to: 'a579217cf7f7f4bf4', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 23434\ntool_uses: 16\nduration_ms: 150042</usage>"}

{"type": "text", "text": "All edge cases pass across 2D/3D shapes, extreme values, boundary conditions, clip=None, all-mask, and varied label_smoothing/delta/clip values.\n\n## Summary\n\nI reverse-engineered all 11 `reforacle` functions by probing and verified each with `compare()` at n≥300 (many at 400-500), plus extensive edge-case runs. **All 11 functions PASS.**\n\n### Deliverable: `/app/part5.py`\n\n```python\nfrom __future__ import annotations\n\nimport torch\nimport torch.nn.functional as F\n\n\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):\n    logits = beta * ((pc - rc) - (pr - rr))\n    ls = label_smoothing\n    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)\n    return loss.mean()\n\n\ndef ipo_loss(pc, pr, rc, rr, beta):\n    logits = (pc - rc) - (pr - rr)\n    loss = (logits - 1.0 / (2.0 * beta)) ** 2\n    return loss.mean()\n\n\ndef kl_penalty(logp, ref_logp, estimator):\n    d = logp - ref_logp\n    if estimator == \"k1\":\n        return d\n    if estimator == \"k2\":\n        return 0.5 * d * d\n    if estimator == \"k3\":\n        return torch.exp(-d) - 1.0 + d\n    raise ValueError(estimator)\n\n\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):\n    ratio = torch.exp(logp - old_logp)\n    l1 = ratio * advantages\n    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages\n    m = torch.min(l1, l2)\n    masked = (m * mask).sum() / mask.sum()\n    return -masked\n\n\ndef value_loss(values, old_values, returns, clip):\n    vclip = old_values + torch.clamp(values - old_values, -clip, clip)\n    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()\n    return loss\n\n\ndef reverse_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return torch.exp(-d) - 1.0 + d\n\n\ndef symmetric_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0\n\n\ndef importance_ratio(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    if clip is not None:\n        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)\n    return ratio\n\n\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):\n    return beta * (chosen_reward - rejected_reward)\n\n\ndef huber_value_loss(values, returns, delta):\n    return F.huber_loss(values, returns, delta=delta)\n\n\ndef clip_fraction(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)\n    return clipped.float().mean()\n```\n\n### Per-function results (all PASS)\n| Function | Result | Key findings |\n|---|---|---|\n| `dpo_loss` | PASS 300/300 | Mean over batch → scalar; sign `-(1-ls)·logσ(logits) - ls·logσ(-logits)` |\n| `ipo_loss` | PASS 300/300 | `((pc-rc)-(pr-rr) - 1/(2β))²`, mean → scalar |\n| `kl_penalty` | PASS 400/400 | Per-element (no reduction); `d=logp-ref`; k1=d, k2=0.5d², k3=exp(-d)-1+d; unknown estimator → `ValueError` |\n| `clipped_pg_loss` | PASS 300/300 | `clip_low/clip_high` are epsilons (bounds `1-cl`..`1+ch`); `-masked_mean(min(l1,l2))` → scalar |\n| `value_loss` | PASS 300/300 | `0.5·mean(max((v-ret)²,(vclip-ret)²))`, 0.5 factor present |\n| `reverse_kl` | PASS 300/300 | Per-element k3 form: `exp(-d)-1+d`, d=logp-ref |\n| `symmetric_kl` | PASS 300/300 | Per-element `0.5·(exp(d)+exp(-d))-1` = ½(reverse+forward k3) |\n| `importance_ratio` | PASS 300/300 | `exp(logp-old)`, clamp to `[1-clip,1+clip]` only if clip not None |\n| `bradley_terry_logit` | PASS 300/300 | Just the logit `β·(cr-rr)`, per-element (no logsigmoid) |\n| `huber_value_loss` | PASS 400/400 | `F.huber_loss` (delta·(|x|-0.5delta) form), **not** smooth_l1 , no extra 0.5 |\n| `clip_fraction` | PASS 400/400 | `mean((ratio > 1+clip) \\| (ratio < 1-clip))` , NOT `\\|ratio-1\\|>clip` (differs at float boundary) |\n\nThe most subtle finding: `clip_fraction` uses separate `>`/`<` bound comparisons rather than `abs(ratio-1) > clip`; these diverge at float32 boundaries (e.g. `1+0.2` rounds to `1.20000004768`, so a ratio equal to it is not counted). I verified this with crafted boundary inputs.\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: aea930bae11f8f34f (use SendMessage with to: 'aea930bae11f8f34f', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29879\ntool_uses: 15\nduration_ms: 151628</usage>"}

{"type": "text", "text": "All 7 functions implemented and verified. `/app/part4.py` is standalone (only `import torch`, no reforacle).\n\n## Key findings from probing\n\n- **Time axis is dim 0** (first dim) for `gae`/`discounted_returns`/`lambda_returns`, not the last dim. For 2D input shape is `(T, B)`; recursion runs backward over dim 0. `next_value` is a scalar or `(B,)` tensor used as the bootstrap `V_{T}` for the final step. `values[t]` becomes the next-value as we recurse backward.\n- **grpo_advantages**: contiguous groups of `group_size` along the flattened rewards; std is **biased** (`unbiased=False`); `eps = 1e-6` applied **outside** the sqrt (`adv/(std+1e-6)`); output is **flattened to 1D** regardless of input shape.\n- **rloo_advantages**: factor is exactly `n/(n-1)` times `(r - group_mean)`; output flattened to 1D.\n- **group_mean_baseline**: `r - group_mean`, no std; output flattened to 1D.\n- **advantage_mean_std**: returns a **stacked tensor `[mean, std]`** (order mean, std). It is **mask-weighted** (mask used as weights, not boolean): `mean = Σ(w·x)/Σw`, `std = sqrt(Σ(w·(x-mean)²)/Σw)` (**biased**, divide by `Σw`). Empty mask → `[0, 0]` (via nan handling); single element → `[x, 0]`.\n\n## Per-function results (compare n≥300 each, atol=1e-6/rtol=1e-5)\n\n| Function | Cases tested | Result |\n|---|---|---|\n| grpo_advantages | no-std, std, 2D, small-std, gs=1 | PASS |\n| gae | 1D & 2D × 5 (gamma,lam) combos incl. edge 0.0/1.0 | PASS |\n| discounted_returns | 1D & 2D × gamma∈{0.9,0.99,1.0,0.0} | PASS |\n| lambda_returns | 1D & 2D × 3 combos | PASS |\n| rloo_advantages | gs=3 1D, gs=5 2D | PASS |\n| group_mean_baseline | gs=4 1D, gs=3 2D | PASS |\n| advantage_mean_std | bool/frac/2D masks, empty, single-elem | PASS |\n\nAll 39 test configurations passed (100%). Full source of `/app/part4.py`:\n\n```python\nimport torch\n\n\ndef grpo_advantages(rewards, group_size, scale_by_std):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = groups - mean\n    if scale_by_std:\n        std = groups.std(dim=1, unbiased=False, keepdim=True)\n        adv = adv / (std + 1e-6)\n    return adv.reshape(-1)\n\n\ndef gae(rewards, values, next_value, gamma, lam):\n    T = rewards.shape[0]\n    advantages = torch.zeros_like(rewards)\n    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    next_v = next_value\n    for t in range(T - 1, -1, -1):\n        delta = rewards[t] + gamma * next_v - values[t]\n        last_adv = delta + gamma * lam * last_adv\n        advantages[t] = last_adv\n        next_v = values[t]\n    return advantages\n\n\ndef discounted_returns(rewards, gamma):\n    T = rewards.shape[0]\n    returns = torch.zeros_like(rewards)\n    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    for t in range(T - 1, -1, -1):\n        acc = rewards[t] + gamma * acc\n        returns[t] = acc\n    return returns\n\n\ndef lambda_returns(rewards, values, next_value, gamma, lam):\n    return gae(rewards, values, next_value, gamma, lam) + values\n\n\ndef rloo_advantages(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = (group_size / (group_size - 1)) * (groups - mean)\n    return adv.reshape(-1)\n\n\ndef group_mean_baseline(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    return (groups - mean).reshape(-1)\n\n\ndef advantage_mean_std(advantages, mask):\n    w = mask\n    wsum = w.sum()\n    mean = (w * advantages).sum() / wsum\n    var = (w * (advantages - mean) ** 2).sum() / wsum\n    std = torch.sqrt(var)\n    result = torch.stack([mean, std])\n    result = torch.nan_to_num(result, nan=0.0)\n    return result\n```\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: afc0516e74454f57b (use SendMessage with to: 'afc0516e74454f57b', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29811\ntool_uses: 22\nduration_ms: 184062</usage>"}

{"type": "text", "text": "All done. Here is the final state.\n\n## Summary\n\nAll 10 functions implemented in pure torch in `/app/part1.py` (standalone, no reforacle import) and verified with `compare()` at n≥300 across multiple shapes plus edge cases (empty/all-zero masks, single elements, negatives, vocab=1).\n\nPass/fail per function (all over many shapes + edge cases):\n- masked_mean: PASS\n- masked_sum: PASS\n- logsumexp: PASS\n- log_softmax: PASS\n- entropy: PASS\n- normalize: PASS\n- whiten: PASS\n- masked_whiten: PASS\n- masked_max: PASS\n- normalized_entropy: PASS\n\nKey conventions discovered:\n- `masked_mean` axis=None: 0.0 fallback on empty mask; axis=int uses `denom.clamp(min=1)` (0/1=0, no keepdim).\n- `masked_sum`: plain `(v*m).sum(dim=axis)`, no special empty handling.\n- `entropy` = masked_mean of per-position softmax entropy over last dim; returns scalar; 0.0 on all-zero mask.\n- `normalized_entropy` = entropy / log(vocab_size) where vocab = last dim; nan when vocab=1 (matches ref).\n- `normalize` = `(x-mean)/(std+eps)` with **unbiased** std.\n- `whiten`: uses **masked** mean and **biased** masked variance, `(v-mean)/sqrt(var+1e-8)`; when `shift_mean=False` adds mean back; denominator clamped to min=1 for empty mask (gives finite values, not nan).\n- `masked_whiten`: same as whiten but multiplies the whitened result by mask **before** the optional mean shift-back , so empty mask yields all zeros.\n- `masked_max`: global max over masked positions (fill unmasked with -inf); special-cases empty mask to 0.0.\n\nFull source of `/app/part1.py`:\n\n```python\nfrom __future__ import annotations\n\nimport math\n\nimport torch\n\n\ndef masked_mean(values, mask, axis=None):\n    if axis is None:\n        denom = mask.sum()\n        if denom == 0:\n            return torch.zeros((), dtype=values.dtype, device=values.device)\n        return (values * mask).sum() / denom\n    num = (values * mask).sum(dim=axis)\n    denom = mask.sum(dim=axis)\n    return num / denom.clamp(min=1)\n\n\ndef masked_sum(values, mask, axis=None):\n    if axis is None:\n        return (values * mask).sum()\n    return (values * mask).sum(dim=axis)\n\n\ndef logsumexp(x, axis):\n    return torch.logsumexp(x, dim=axis)\n\n\ndef log_softmax(x, axis):\n    return torch.log_softmax(x, dim=axis)\n\n\ndef entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom\n\n\ndef normalize(x, eps):\n    return (x - x.mean()) / (x.std() + eps)\n\n\ndef whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    out = out * mask\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_max(values, mask):\n    if mask.sum() == 0:\n        return torch.zeros((), dtype=values.dtype, device=values.device)\n    filled = values.masked_fill(mask == 0, float(\"-inf\"))\n    return filled.max()\n\n\ndef normalized_entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    vocab = logits.shape[-1]\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom / math.log(vocab)\n```"}

{"type": "text", "text": "agentId: a8ab0e0c2a3fc9eb3 (use SendMessage with to: 'a8ab0e0c2a3fc9eb3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 37980\ntool_uses: 33\nduration_ms: 262016</usage>"}

{"type": "text", "text": "All 10 functions reverse-engineered and verified. Here is the final report.\n\n## Summary\n\nI reverse-engineered all 10 `reforacle` functions by probing with varied shapes, dtypes, signs, and edge cases, then verified each against the oracle with `compare()` at n≥300 (plus larger stress runs).\n\n### Per-function pass/fail (all PASS)\n```\ncumulative_max ...... PASS  (1D, 2D, int, single-elem)\nquantile_lower ...... PASS  (1D, 2D, q=0/1, single-row/col)\nmedian_reward ....... PASS  (1D, 2D, single)\nmode_label .......... PASS  (1D, 2D, ties, all-same, single)\nargmax_tokens ....... PASS  (1D, 2D, single-elem last dim)\nfirst_nonzero_index . PASS  (binary/frac/int/count masks, 1D+2D, all-zero)\npad_mask_from_lengths PASS  (normal, len>max_len, zeros)\nbucketize_reward .... PASS  (random, exact boundaries, empty boundaries)\ntop_k_mask .......... PASS  (1D, 2D, k>n, ties, k=0 raises)\ntop_p_mask .......... PASS  (1D, 2D, straddle, peaky, uniform)\n```\n\n### Key conventions discovered (the non-obvious ones)\n- **cumulative_max**: NOT a normal cummax. It is an *exclusive/shifted* cummax along dim 0: `out[0]=x[0]`, `out[i]=max(x[0..i-1])`. Returns values only (no tuple).\n- **quantile_lower / median_reward (2D)**: operate along dim 0 but in a peculiar way , they **sort each row**, then median/quantile is taken over rows *by original row index*. median = average of `sort(row[(n-1)//2])` and `sort(row[n//2])`; quantile_lower = `sort(row[floor(q*(n-1))])`. (1D uses plain `torch.quantile` with `interpolation='lower'`/`'linear'`.)\n- **mode_label**: most frequent label, ties broken to the **larger** value (opposite of `torch.mode`); per-row for 2D; scalar int64.\n- **first_nonzero_index**: implemented as the buggy idiom `argmax(mask.long() * arange(n,0,-1))` with a `sum(mask) <= 0 → -1` guard. For a true 0/1 mask this equals first-nonzero, but values are truncated-to-long and position-weighted, so it's only equivalent for proper masks. Per-row for 2D, -1 if a row sums to ≤0.\n- **bucketize_reward**: `torch.bucketize(..., right=True)`.\n- **top_k_mask**: returns a **bool** mask via threshold `logits >= kth-largest-value` (so ties can select >k elements); `k` clamped to `min(k, n)` (k>n → all True); `k=0` raises RuntimeError.\n- **top_p_mask**: returns **renormalized probabilities** (kept elements sum to 1, excluded set to 0), NOT a mask. Inclusion rule uses the *exclusive* cumsum of descending-sorted probs: keep where `cumsum_before_token < p`, always keeping the top-1.\n\nDeliverable written to `/app/part2.py` (standalone, imports only `torch`; the only \"reforacle\" mention is in a comment). Full source is shown above. `/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: ab8a55331340147b3 (use SendMessage with to: 'ab8a55331340147b3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 138643\ntool_uses: 112\nduration_ms: 1361957</usage>"}
Agent
{
  "description": "Reverse-engineer reduction primitives",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`) to reproduce its exact numerical behavior in pure `torch`. You CANNOT read its source; only call it and compare.\n\nThere is a helper at /app/harness.py: `from harness import compare` , `compare(ref_fn, cand_fn, make_inputs, n=300)` calls `make_inputs()` (returns a tuple of args, using FRESH random tensors each call) n times, runs both functions, and reports whether they match to atol=1e-6, rtol=1e-5. It also matches raised-exception types. Use it heavily.\n\nYour job: implement these 10 functions EXACTLY as reforacle does. Probe `reforacle.<name>` with many inputs (varied shapes, dtypes, signs; edge cases like empty masks, single elements, ties, zeros) to nail the exact convention (mean vs sum reduction, biased vs unbiased std, eps placement, sign, output shape/dtype, keepdim, how axis=None vs int is handled, what happens with all-zero mask).\n\nSignatures (keep EXACTLY):\n```\ndef masked_mean(values, mask, axis=None):\ndef masked_sum(values, mask, axis=None):\ndef logsumexp(x, axis):\ndef log_softmax(x, axis):\ndef entropy(logits, mask):        # likely entropy of softmax(logits) over last dim, then masked-reduced by mask; PROBE shapes carefully\ndef normalize(x, eps):            # (x-mean)/(std+eps); std is UNBIASED (torch default). Verify.\ndef whiten(values, mask, shift_mean):   # whitening; PROBE role of mask and shift_mean bool\ndef masked_whiten(values, mask, shift_mean):\ndef masked_max(values, mask):\ndef normalized_entropy(logits, mask):\n```\n\nKnown facts already confirmed: `masked_mean(values,mask,axis=None)` = sum(values*mask)/sum(mask), returns 0.0 (not nan) when mask sums to 0. `masked_mean` with axis=int reduces along that axis (no keepdim). `normalize` uses unbiased std. For entropy/normalized_entropy, carefully probe input shape , logits likely (..., vocab) and mask over the leading token dims; figure out exactly what reduction is applied and whether it returns a scalar or per-position. normalized_entropy likely divides entropy by log(vocab_size).\n\nDeliverables:\n1. Write file /app/part1.py containing ONLY `import torch` (plus `from __future__ import annotations`) and the 10 function definitions in PURE torch (NO reforacle import). It must be standalone.\n2. Verify EVERY function with compare() over n>=300 across multiple input shapes AND edge cases. Iterate until all pass robustly. For entropy-type functions test both float and where mask is all zeros.\n3. In your final message, paste the FULL final source of /app/part1.py and a one-line pass/fail summary per function.\n\nDo not modify /app/objectives.py. Be rigorous: passing your own random tests but failing held-out grading is the failure mode to avoid , test broadly.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 6 functions pass across shapes and edge cases. Done.\n\n## Summary\n\nReverse-engineered all 6 functions and wrote `/app/part3.py` (pure torch, no reforacle import). Verified each with `compare()` at n≥300 across (B,T,V) and (N,V) shapes plus edge cases.\n\n**Per-function results (all PASS):**\n\n| Function | Behavior discovered | Result |\n|---|---|---|\n| `token_logprobs` | `log_softmax(-1).gather(labels)` → shape = labels.shape | PASS 300/300 |\n| `selective_logprobs` | token logprobs × mask, then **sum over seq** → shape (B,) | PASS 300/300 |\n| `sequence_logprob` | sum of (logprob×mask) over seq; if `length_normalize` truthy, divide by `mask.sum(-1).clamp(min=1)` (empty mask → 0, not nan) | PASS (both flags + empty-mask) |\n| `smoothed_nll` | `(1-s)*nll + s*(-mean_v logp)` per token, reduced by **mean over all** → scalar | PASS 300/300 |\n| `cross_entropy` | log_softmax, gather on `labels.clamp(min=0)` (so `-100` is safe but an in-range out-of-vocab ignore_index still raises), mask by `labels!=ignore_index`, `sum/mask.sum().clamp(min=1)` → **all-ignored gives 0, not nan** (differs from `F.cross_entropy`). Works for 2D (N,V) and 3D (B,T,V) | PASS 300/300 + all-ignored |\n| `logprob_at_temperature` | `log_softmax(logits/temperature,-1).gather(labels)` | PASS 300/300 |\n\n**Key non-obvious findings:**\n- `selective_logprobs` is a *reduced* value (sum over sequence), shape (B,), not element-wise like `token_logprobs`.\n- `sequence_logprob` normalizes with a `clamp(min=1)` denominator, so empty masks yield 0 rather than nan.\n- `cross_entropy` does **not** wrap `F.cross_entropy`: it clamps negatives before gather and uses a `clamp(min=1)` denominator, giving **0 for the all-ignored case** where `F.cross_entropy` returns nan.\n\nFull source is at `/app/part3.py`."}

{"type": "text", "text": "agentId: a579217cf7f7f4bf4 (use SendMessage with to: 'a579217cf7f7f4bf4', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 23434\ntool_uses: 16\nduration_ms: 150042</usage>"}

{"type": "text", "text": "All edge cases pass across 2D/3D shapes, extreme values, boundary conditions, clip=None, all-mask, and varied label_smoothing/delta/clip values.\n\n## Summary\n\nI reverse-engineered all 11 `reforacle` functions by probing and verified each with `compare()` at n≥300 (many at 400-500), plus extensive edge-case runs. **All 11 functions PASS.**\n\n### Deliverable: `/app/part5.py`\n\n```python\nfrom __future__ import annotations\n\nimport torch\nimport torch.nn.functional as F\n\n\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):\n    logits = beta * ((pc - rc) - (pr - rr))\n    ls = label_smoothing\n    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)\n    return loss.mean()\n\n\ndef ipo_loss(pc, pr, rc, rr, beta):\n    logits = (pc - rc) - (pr - rr)\n    loss = (logits - 1.0 / (2.0 * beta)) ** 2\n    return loss.mean()\n\n\ndef kl_penalty(logp, ref_logp, estimator):\n    d = logp - ref_logp\n    if estimator == \"k1\":\n        return d\n    if estimator == \"k2\":\n        return 0.5 * d * d\n    if estimator == \"k3\":\n        return torch.exp(-d) - 1.0 + d\n    raise ValueError(estimator)\n\n\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):\n    ratio = torch.exp(logp - old_logp)\n    l1 = ratio * advantages\n    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages\n    m = torch.min(l1, l2)\n    masked = (m * mask).sum() / mask.sum()\n    return -masked\n\n\ndef value_loss(values, old_values, returns, clip):\n    vclip = old_values + torch.clamp(values - old_values, -clip, clip)\n    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()\n    return loss\n\n\ndef reverse_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return torch.exp(-d) - 1.0 + d\n\n\ndef symmetric_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0\n\n\ndef importance_ratio(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    if clip is not None:\n        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)\n    return ratio\n\n\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):\n    return beta * (chosen_reward - rejected_reward)\n\n\ndef huber_value_loss(values, returns, delta):\n    return F.huber_loss(values, returns, delta=delta)\n\n\ndef clip_fraction(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)\n    return clipped.float().mean()\n```\n\n### Per-function results (all PASS)\n| Function | Result | Key findings |\n|---|---|---|\n| `dpo_loss` | PASS 300/300 | Mean over batch → scalar; sign `-(1-ls)·logσ(logits) - ls·logσ(-logits)` |\n| `ipo_loss` | PASS 300/300 | `((pc-rc)-(pr-rr) - 1/(2β))²`, mean → scalar |\n| `kl_penalty` | PASS 400/400 | Per-element (no reduction); `d=logp-ref`; k1=d, k2=0.5d², k3=exp(-d)-1+d; unknown estimator → `ValueError` |\n| `clipped_pg_loss` | PASS 300/300 | `clip_low/clip_high` are epsilons (bounds `1-cl`..`1+ch`); `-masked_mean(min(l1,l2))` → scalar |\n| `value_loss` | PASS 300/300 | `0.5·mean(max((v-ret)²,(vclip-ret)²))`, 0.5 factor present |\n| `reverse_kl` | PASS 300/300 | Per-element k3 form: `exp(-d)-1+d`, d=logp-ref |\n| `symmetric_kl` | PASS 300/300 | Per-element `0.5·(exp(d)+exp(-d))-1` = ½(reverse+forward k3) |\n| `importance_ratio` | PASS 300/300 | `exp(logp-old)`, clamp to `[1-clip,1+clip]` only if clip not None |\n| `bradley_terry_logit` | PASS 300/300 | Just the logit `β·(cr-rr)`, per-element (no logsigmoid) |\n| `huber_value_loss` | PASS 400/400 | `F.huber_loss` (delta·(|x|-0.5delta) form), **not** smooth_l1 , no extra 0.5 |\n| `clip_fraction` | PASS 400/400 | `mean((ratio > 1+clip) \\| (ratio < 1-clip))` , NOT `\\|ratio-1\\|>clip` (differs at float boundary) |\n\nThe most subtle finding: `clip_fraction` uses separate `>`/`<` bound comparisons rather than `abs(ratio-1) > clip`; these diverge at float32 boundaries (e.g. `1+0.2` rounds to `1.20000004768`, so a ratio equal to it is not counted). I verified this with crafted boundary inputs.\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: aea930bae11f8f34f (use SendMessage with to: 'aea930bae11f8f34f', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29879\ntool_uses: 15\nduration_ms: 151628</usage>"}

{"type": "text", "text": "All 7 functions implemented and verified. `/app/part4.py` is standalone (only `import torch`, no reforacle).\n\n## Key findings from probing\n\n- **Time axis is dim 0** (first dim) for `gae`/`discounted_returns`/`lambda_returns`, not the last dim. For 2D input shape is `(T, B)`; recursion runs backward over dim 0. `next_value` is a scalar or `(B,)` tensor used as the bootstrap `V_{T}` for the final step. `values[t]` becomes the next-value as we recurse backward.\n- **grpo_advantages**: contiguous groups of `group_size` along the flattened rewards; std is **biased** (`unbiased=False`); `eps = 1e-6` applied **outside** the sqrt (`adv/(std+1e-6)`); output is **flattened to 1D** regardless of input shape.\n- **rloo_advantages**: factor is exactly `n/(n-1)` times `(r - group_mean)`; output flattened to 1D.\n- **group_mean_baseline**: `r - group_mean`, no std; output flattened to 1D.\n- **advantage_mean_std**: returns a **stacked tensor `[mean, std]`** (order mean, std). It is **mask-weighted** (mask used as weights, not boolean): `mean = Σ(w·x)/Σw`, `std = sqrt(Σ(w·(x-mean)²)/Σw)` (**biased**, divide by `Σw`). Empty mask → `[0, 0]` (via nan handling); single element → `[x, 0]`.\n\n## Per-function results (compare n≥300 each, atol=1e-6/rtol=1e-5)\n\n| Function | Cases tested | Result |\n|---|---|---|\n| grpo_advantages | no-std, std, 2D, small-std, gs=1 | PASS |\n| gae | 1D & 2D × 5 (gamma,lam) combos incl. edge 0.0/1.0 | PASS |\n| discounted_returns | 1D & 2D × gamma∈{0.9,0.99,1.0,0.0} | PASS |\n| lambda_returns | 1D & 2D × 3 combos | PASS |\n| rloo_advantages | gs=3 1D, gs=5 2D | PASS |\n| group_mean_baseline | gs=4 1D, gs=3 2D | PASS |\n| advantage_mean_std | bool/frac/2D masks, empty, single-elem | PASS |\n\nAll 39 test configurations passed (100%). Full source of `/app/part4.py`:\n\n```python\nimport torch\n\n\ndef grpo_advantages(rewards, group_size, scale_by_std):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = groups - mean\n    if scale_by_std:\n        std = groups.std(dim=1, unbiased=False, keepdim=True)\n        adv = adv / (std + 1e-6)\n    return adv.reshape(-1)\n\n\ndef gae(rewards, values, next_value, gamma, lam):\n    T = rewards.shape[0]\n    advantages = torch.zeros_like(rewards)\n    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    next_v = next_value\n    for t in range(T - 1, -1, -1):\n        delta = rewards[t] + gamma * next_v - values[t]\n        last_adv = delta + gamma * lam * last_adv\n        advantages[t] = last_adv\n        next_v = values[t]\n    return advantages\n\n\ndef discounted_returns(rewards, gamma):\n    T = rewards.shape[0]\n    returns = torch.zeros_like(rewards)\n    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    for t in range(T - 1, -1, -1):\n        acc = rewards[t] + gamma * acc\n        returns[t] = acc\n    return returns\n\n\ndef lambda_returns(rewards, values, next_value, gamma, lam):\n    return gae(rewards, values, next_value, gamma, lam) + values\n\n\ndef rloo_advantages(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = (group_size / (group_size - 1)) * (groups - mean)\n    return adv.reshape(-1)\n\n\ndef group_mean_baseline(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    return (groups - mean).reshape(-1)\n\n\ndef advantage_mean_std(advantages, mask):\n    w = mask\n    wsum = w.sum()\n    mean = (w * advantages).sum() / wsum\n    var = (w * (advantages - mean) ** 2).sum() / wsum\n    std = torch.sqrt(var)\n    result = torch.stack([mean, std])\n    result = torch.nan_to_num(result, nan=0.0)\n    return result\n```\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: afc0516e74454f57b (use SendMessage with to: 'afc0516e74454f57b', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29811\ntool_uses: 22\nduration_ms: 184062</usage>"}

{"type": "text", "text": "All done. Here is the final state.\n\n## Summary\n\nAll 10 functions implemented in pure torch in `/app/part1.py` (standalone, no reforacle import) and verified with `compare()` at n≥300 across multiple shapes plus edge cases (empty/all-zero masks, single elements, negatives, vocab=1).\n\nPass/fail per function (all over many shapes + edge cases):\n- masked_mean: PASS\n- masked_sum: PASS\n- logsumexp: PASS\n- log_softmax: PASS\n- entropy: PASS\n- normalize: PASS\n- whiten: PASS\n- masked_whiten: PASS\n- masked_max: PASS\n- normalized_entropy: PASS\n\nKey conventions discovered:\n- `masked_mean` axis=None: 0.0 fallback on empty mask; axis=int uses `denom.clamp(min=1)` (0/1=0, no keepdim).\n- `masked_sum`: plain `(v*m).sum(dim=axis)`, no special empty handling.\n- `entropy` = masked_mean of per-position softmax entropy over last dim; returns scalar; 0.0 on all-zero mask.\n- `normalized_entropy` = entropy / log(vocab_size) where vocab = last dim; nan when vocab=1 (matches ref).\n- `normalize` = `(x-mean)/(std+eps)` with **unbiased** std.\n- `whiten`: uses **masked** mean and **biased** masked variance, `(v-mean)/sqrt(var+1e-8)`; when `shift_mean=False` adds mean back; denominator clamped to min=1 for empty mask (gives finite values, not nan).\n- `masked_whiten`: same as whiten but multiplies the whitened result by mask **before** the optional mean shift-back , so empty mask yields all zeros.\n- `masked_max`: global max over masked positions (fill unmasked with -inf); special-cases empty mask to 0.0.\n\nFull source of `/app/part1.py`:\n\n```python\nfrom __future__ import annotations\n\nimport math\n\nimport torch\n\n\ndef masked_mean(values, mask, axis=None):\n    if axis is None:\n        denom = mask.sum()\n        if denom == 0:\n            return torch.zeros((), dtype=values.dtype, device=values.device)\n        return (values * mask).sum() / denom\n    num = (values * mask).sum(dim=axis)\n    denom = mask.sum(dim=axis)\n    return num / denom.clamp(min=1)\n\n\ndef masked_sum(values, mask, axis=None):\n    if axis is None:\n        return (values * mask).sum()\n    return (values * mask).sum(dim=axis)\n\n\ndef logsumexp(x, axis):\n    return torch.logsumexp(x, dim=axis)\n\n\ndef log_softmax(x, axis):\n    return torch.log_softmax(x, dim=axis)\n\n\ndef entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom\n\n\ndef normalize(x, eps):\n    return (x - x.mean()) / (x.std() + eps)\n\n\ndef whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    out = out * mask\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_max(values, mask):\n    if mask.sum() == 0:\n        return torch.zeros((), dtype=values.dtype, device=values.device)\n    filled = values.masked_fill(mask == 0, float(\"-inf\"))\n    return filled.max()\n\n\ndef normalized_entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    vocab = logits.shape[-1]\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom / math.log(vocab)\n```"}

{"type": "text", "text": "agentId: a8ab0e0c2a3fc9eb3 (use SendMessage with to: 'a8ab0e0c2a3fc9eb3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 37980\ntool_uses: 33\nduration_ms: 262016</usage>"}

{"type": "text", "text": "All 10 functions reverse-engineered and verified. Here is the final report.\n\n## Summary\n\nI reverse-engineered all 10 `reforacle` functions by probing with varied shapes, dtypes, signs, and edge cases, then verified each against the oracle with `compare()` at n≥300 (plus larger stress runs).\n\n### Per-function pass/fail (all PASS)\n```\ncumulative_max ...... PASS  (1D, 2D, int, single-elem)\nquantile_lower ...... PASS  (1D, 2D, q=0/1, single-row/col)\nmedian_reward ....... PASS  (1D, 2D, single)\nmode_label .......... PASS  (1D, 2D, ties, all-same, single)\nargmax_tokens ....... PASS  (1D, 2D, single-elem last dim)\nfirst_nonzero_index . PASS  (binary/frac/int/count masks, 1D+2D, all-zero)\npad_mask_from_lengths PASS  (normal, len>max_len, zeros)\nbucketize_reward .... PASS  (random, exact boundaries, empty boundaries)\ntop_k_mask .......... PASS  (1D, 2D, k>n, ties, k=0 raises)\ntop_p_mask .......... PASS  (1D, 2D, straddle, peaky, uniform)\n```\n\n### Key conventions discovered (the non-obvious ones)\n- **cumulative_max**: NOT a normal cummax. It is an *exclusive/shifted* cummax along dim 0: `out[0]=x[0]`, `out[i]=max(x[0..i-1])`. Returns values only (no tuple).\n- **quantile_lower / median_reward (2D)**: operate along dim 0 but in a peculiar way , they **sort each row**, then median/quantile is taken over rows *by original row index*. median = average of `sort(row[(n-1)//2])` and `sort(row[n//2])`; quantile_lower = `sort(row[floor(q*(n-1))])`. (1D uses plain `torch.quantile` with `interpolation='lower'`/`'linear'`.)\n- **mode_label**: most frequent label, ties broken to the **larger** value (opposite of `torch.mode`); per-row for 2D; scalar int64.\n- **first_nonzero_index**: implemented as the buggy idiom `argmax(mask.long() * arange(n,0,-1))` with a `sum(mask) <= 0 → -1` guard. For a true 0/1 mask this equals first-nonzero, but values are truncated-to-long and position-weighted, so it's only equivalent for proper masks. Per-row for 2D, -1 if a row sums to ≤0.\n- **bucketize_reward**: `torch.bucketize(..., right=True)`.\n- **top_k_mask**: returns a **bool** mask via threshold `logits >= kth-largest-value` (so ties can select >k elements); `k` clamped to `min(k, n)` (k>n → all True); `k=0` raises RuntimeError.\n- **top_p_mask**: returns **renormalized probabilities** (kept elements sum to 1, excluded set to 0), NOT a mask. Inclusion rule uses the *exclusive* cumsum of descending-sorted probs: keep where `cumsum_before_token < p`, always keeping the top-1.\n\nDeliverable written to `/app/part2.py` (standalone, imports only `torch`; the only \"reforacle\" mention is in a comment). Full source is shown above. `/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: ab8a55331340147b3 (use SendMessage with to: 'ab8a55331340147b3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 138643\ntool_uses: 112\nduration_ms: 1361957</usage>"}
Agent
{
  "description": "Reverse-engineer misc primitives",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`) to reproduce its exact numerical behavior in pure `torch`. You CANNOT read its source; only call it and compare.\n\nHelper at /app/harness.py: `from harness import compare` , `compare(ref_fn, cand_fn, make_inputs, n=300)` calls `make_inputs()` (returns tuple of args with FRESH random tensors each call) n times and reports match (atol=1e-6, rtol=1e-5), also matching exception types. For integer/index outputs it compares exactly. Use it heavily.\n\nImplement these 10 functions EXACTLY as reforacle does. Probe with varied shapes/dtypes/signs and edge cases (ties, empty, single element, out-of-range).\n\nSignatures (keep EXACTLY):\n```\ndef cumulative_max(x):                        # cummax along... which dim? probe 1D and 2D. Return values only or tuple? PROBE.\ndef quantile_lower(x, q):                     # torch.quantile with interpolation='lower'? PROBE q in [0,1]\ndef median_reward(rewards):                   # torch.median (lower median) vs mean-of-two? PROBE even length\ndef mode_label(labels):                       # most frequent label; tie-break convention? PROBE. output dtype/scalar?\ndef argmax_tokens(logits):                    # argmax over last dim\ndef first_nonzero_index(mask):                # index of first nonzero; per-row for 2D? behavior if all zero? PROBE\ndef pad_mask_from_lengths(lengths, max_len):  # produce mask from lengths; dtype? shape (len(lengths), max_len)? mask = position<length? PROBE\ndef bucketize_reward(rewards, boundaries):    # torch.bucketize; right=? PROBE boundary values\ndef top_k_mask(logits, k):                    # keep top-k per last dim; returns mask (bool/float) or masked logits (-inf)? PROBE\ndef top_p_mask(probs, p):                     # nucleus mask; returns mask (bool/float)? which elements kept? sorted-cumsum convention (include first crossing?). PROBE carefully\n```\n\nFor each: determine exact output dtype and shape by inspecting reforacle output. For cumulative_max and median, check whether a tuple (values, indices) is returned. For top_k_mask/top_p_mask determine whether output is a boolean mask, float mask, or the logits/probs with excluded set to -inf/0 , probe by printing reforacle output values. For top_p, determine the exact inclusion rule (the standard is: sort descending, cumsum, keep tokens where cumsum <= p but always keep at least the top-1; some impls shift the mask to include the first token that crosses p). Test with distributions that straddle the boundary.\n\nDeliverables:\n1. Write /app/part2.py: `import torch` + the 10 pure-torch definitions (NO reforacle import), standalone.\n2. Verify each with compare() n>=300 across shapes and edge cases; iterate to robust pass.\n3. Final message: paste FULL final /app/part2.py source + per-function pass/fail line.\n\nDo not modify /app/objectives.py.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 6 functions pass across shapes and edge cases. Done.\n\n## Summary\n\nReverse-engineered all 6 functions and wrote `/app/part3.py` (pure torch, no reforacle import). Verified each with `compare()` at n≥300 across (B,T,V) and (N,V) shapes plus edge cases.\n\n**Per-function results (all PASS):**\n\n| Function | Behavior discovered | Result |\n|---|---|---|\n| `token_logprobs` | `log_softmax(-1).gather(labels)` → shape = labels.shape | PASS 300/300 |\n| `selective_logprobs` | token logprobs × mask, then **sum over seq** → shape (B,) | PASS 300/300 |\n| `sequence_logprob` | sum of (logprob×mask) over seq; if `length_normalize` truthy, divide by `mask.sum(-1).clamp(min=1)` (empty mask → 0, not nan) | PASS (both flags + empty-mask) |\n| `smoothed_nll` | `(1-s)*nll + s*(-mean_v logp)` per token, reduced by **mean over all** → scalar | PASS 300/300 |\n| `cross_entropy` | log_softmax, gather on `labels.clamp(min=0)` (so `-100` is safe but an in-range out-of-vocab ignore_index still raises), mask by `labels!=ignore_index`, `sum/mask.sum().clamp(min=1)` → **all-ignored gives 0, not nan** (differs from `F.cross_entropy`). Works for 2D (N,V) and 3D (B,T,V) | PASS 300/300 + all-ignored |\n| `logprob_at_temperature` | `log_softmax(logits/temperature,-1).gather(labels)` | PASS 300/300 |\n\n**Key non-obvious findings:**\n- `selective_logprobs` is a *reduced* value (sum over sequence), shape (B,), not element-wise like `token_logprobs`.\n- `sequence_logprob` normalizes with a `clamp(min=1)` denominator, so empty masks yield 0 rather than nan.\n- `cross_entropy` does **not** wrap `F.cross_entropy`: it clamps negatives before gather and uses a `clamp(min=1)` denominator, giving **0 for the all-ignored case** where `F.cross_entropy` returns nan.\n\nFull source is at `/app/part3.py`."}

{"type": "text", "text": "agentId: a579217cf7f7f4bf4 (use SendMessage with to: 'a579217cf7f7f4bf4', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 23434\ntool_uses: 16\nduration_ms: 150042</usage>"}

{"type": "text", "text": "All edge cases pass across 2D/3D shapes, extreme values, boundary conditions, clip=None, all-mask, and varied label_smoothing/delta/clip values.\n\n## Summary\n\nI reverse-engineered all 11 `reforacle` functions by probing and verified each with `compare()` at n≥300 (many at 400-500), plus extensive edge-case runs. **All 11 functions PASS.**\n\n### Deliverable: `/app/part5.py`\n\n```python\nfrom __future__ import annotations\n\nimport torch\nimport torch.nn.functional as F\n\n\ndef dpo_loss(pc, pr, rc, rr, beta, label_smoothing):\n    logits = beta * ((pc - rc) - (pr - rr))\n    ls = label_smoothing\n    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)\n    return loss.mean()\n\n\ndef ipo_loss(pc, pr, rc, rr, beta):\n    logits = (pc - rc) - (pr - rr)\n    loss = (logits - 1.0 / (2.0 * beta)) ** 2\n    return loss.mean()\n\n\ndef kl_penalty(logp, ref_logp, estimator):\n    d = logp - ref_logp\n    if estimator == \"k1\":\n        return d\n    if estimator == \"k2\":\n        return 0.5 * d * d\n    if estimator == \"k3\":\n        return torch.exp(-d) - 1.0 + d\n    raise ValueError(estimator)\n\n\ndef clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):\n    ratio = torch.exp(logp - old_logp)\n    l1 = ratio * advantages\n    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages\n    m = torch.min(l1, l2)\n    masked = (m * mask).sum() / mask.sum()\n    return -masked\n\n\ndef value_loss(values, old_values, returns, clip):\n    vclip = old_values + torch.clamp(values - old_values, -clip, clip)\n    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()\n    return loss\n\n\ndef reverse_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return torch.exp(-d) - 1.0 + d\n\n\ndef symmetric_kl(logp, ref_logp):\n    d = logp - ref_logp\n    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0\n\n\ndef importance_ratio(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    if clip is not None:\n        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)\n    return ratio\n\n\ndef bradley_terry_logit(chosen_reward, rejected_reward, beta):\n    return beta * (chosen_reward - rejected_reward)\n\n\ndef huber_value_loss(values, returns, delta):\n    return F.huber_loss(values, returns, delta=delta)\n\n\ndef clip_fraction(logp, old_logp, clip):\n    ratio = torch.exp(logp - old_logp)\n    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)\n    return clipped.float().mean()\n```\n\n### Per-function results (all PASS)\n| Function | Result | Key findings |\n|---|---|---|\n| `dpo_loss` | PASS 300/300 | Mean over batch → scalar; sign `-(1-ls)·logσ(logits) - ls·logσ(-logits)` |\n| `ipo_loss` | PASS 300/300 | `((pc-rc)-(pr-rr) - 1/(2β))²`, mean → scalar |\n| `kl_penalty` | PASS 400/400 | Per-element (no reduction); `d=logp-ref`; k1=d, k2=0.5d², k3=exp(-d)-1+d; unknown estimator → `ValueError` |\n| `clipped_pg_loss` | PASS 300/300 | `clip_low/clip_high` are epsilons (bounds `1-cl`..`1+ch`); `-masked_mean(min(l1,l2))` → scalar |\n| `value_loss` | PASS 300/300 | `0.5·mean(max((v-ret)²,(vclip-ret)²))`, 0.5 factor present |\n| `reverse_kl` | PASS 300/300 | Per-element k3 form: `exp(-d)-1+d`, d=logp-ref |\n| `symmetric_kl` | PASS 300/300 | Per-element `0.5·(exp(d)+exp(-d))-1` = ½(reverse+forward k3) |\n| `importance_ratio` | PASS 300/300 | `exp(logp-old)`, clamp to `[1-clip,1+clip]` only if clip not None |\n| `bradley_terry_logit` | PASS 300/300 | Just the logit `β·(cr-rr)`, per-element (no logsigmoid) |\n| `huber_value_loss` | PASS 400/400 | `F.huber_loss` (delta·(|x|-0.5delta) form), **not** smooth_l1 , no extra 0.5 |\n| `clip_fraction` | PASS 400/400 | `mean((ratio > 1+clip) \\| (ratio < 1-clip))` , NOT `\\|ratio-1\\|>clip` (differs at float boundary) |\n\nThe most subtle finding: `clip_fraction` uses separate `>`/`<` bound comparisons rather than `abs(ratio-1) > clip`; these diverge at float32 boundaries (e.g. `1+0.2` rounds to `1.20000004768`, so a ratio equal to it is not counted). I verified this with crafted boundary inputs.\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: aea930bae11f8f34f (use SendMessage with to: 'aea930bae11f8f34f', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29879\ntool_uses: 15\nduration_ms: 151628</usage>"}

{"type": "text", "text": "All 7 functions implemented and verified. `/app/part4.py` is standalone (only `import torch`, no reforacle).\n\n## Key findings from probing\n\n- **Time axis is dim 0** (first dim) for `gae`/`discounted_returns`/`lambda_returns`, not the last dim. For 2D input shape is `(T, B)`; recursion runs backward over dim 0. `next_value` is a scalar or `(B,)` tensor used as the bootstrap `V_{T}` for the final step. `values[t]` becomes the next-value as we recurse backward.\n- **grpo_advantages**: contiguous groups of `group_size` along the flattened rewards; std is **biased** (`unbiased=False`); `eps = 1e-6` applied **outside** the sqrt (`adv/(std+1e-6)`); output is **flattened to 1D** regardless of input shape.\n- **rloo_advantages**: factor is exactly `n/(n-1)` times `(r - group_mean)`; output flattened to 1D.\n- **group_mean_baseline**: `r - group_mean`, no std; output flattened to 1D.\n- **advantage_mean_std**: returns a **stacked tensor `[mean, std]`** (order mean, std). It is **mask-weighted** (mask used as weights, not boolean): `mean = Σ(w·x)/Σw`, `std = sqrt(Σ(w·(x-mean)²)/Σw)` (**biased**, divide by `Σw`). Empty mask → `[0, 0]` (via nan handling); single element → `[x, 0]`.\n\n## Per-function results (compare n≥300 each, atol=1e-6/rtol=1e-5)\n\n| Function | Cases tested | Result |\n|---|---|---|\n| grpo_advantages | no-std, std, 2D, small-std, gs=1 | PASS |\n| gae | 1D & 2D × 5 (gamma,lam) combos incl. edge 0.0/1.0 | PASS |\n| discounted_returns | 1D & 2D × gamma∈{0.9,0.99,1.0,0.0} | PASS |\n| lambda_returns | 1D & 2D × 3 combos | PASS |\n| rloo_advantages | gs=3 1D, gs=5 2D | PASS |\n| group_mean_baseline | gs=4 1D, gs=3 2D | PASS |\n| advantage_mean_std | bool/frac/2D masks, empty, single-elem | PASS |\n\nAll 39 test configurations passed (100%). Full source of `/app/part4.py`:\n\n```python\nimport torch\n\n\ndef grpo_advantages(rewards, group_size, scale_by_std):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = groups - mean\n    if scale_by_std:\n        std = groups.std(dim=1, unbiased=False, keepdim=True)\n        adv = adv / (std + 1e-6)\n    return adv.reshape(-1)\n\n\ndef gae(rewards, values, next_value, gamma, lam):\n    T = rewards.shape[0]\n    advantages = torch.zeros_like(rewards)\n    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    next_v = next_value\n    for t in range(T - 1, -1, -1):\n        delta = rewards[t] + gamma * next_v - values[t]\n        last_adv = delta + gamma * lam * last_adv\n        advantages[t] = last_adv\n        next_v = values[t]\n    return advantages\n\n\ndef discounted_returns(rewards, gamma):\n    T = rewards.shape[0]\n    returns = torch.zeros_like(rewards)\n    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)\n    for t in range(T - 1, -1, -1):\n        acc = rewards[t] + gamma * acc\n        returns[t] = acc\n    return returns\n\n\ndef lambda_returns(rewards, values, next_value, gamma, lam):\n    return gae(rewards, values, next_value, gamma, lam) + values\n\n\ndef rloo_advantages(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    adv = (group_size / (group_size - 1)) * (groups - mean)\n    return adv.reshape(-1)\n\n\ndef group_mean_baseline(rewards, group_size):\n    flat = rewards.reshape(-1)\n    groups = flat.reshape(-1, group_size)\n    mean = groups.mean(dim=1, keepdim=True)\n    return (groups - mean).reshape(-1)\n\n\ndef advantage_mean_std(advantages, mask):\n    w = mask\n    wsum = w.sum()\n    mean = (w * advantages).sum() / wsum\n    var = (w * (advantages - mean) ** 2).sum() / wsum\n    std = torch.sqrt(var)\n    result = torch.stack([mean, std])\n    result = torch.nan_to_num(result, nan=0.0)\n    return result\n```\n\n`/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: afc0516e74454f57b (use SendMessage with to: 'afc0516e74454f57b', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29811\ntool_uses: 22\nduration_ms: 184062</usage>"}

{"type": "text", "text": "All done. Here is the final state.\n\n## Summary\n\nAll 10 functions implemented in pure torch in `/app/part1.py` (standalone, no reforacle import) and verified with `compare()` at n≥300 across multiple shapes plus edge cases (empty/all-zero masks, single elements, negatives, vocab=1).\n\nPass/fail per function (all over many shapes + edge cases):\n- masked_mean: PASS\n- masked_sum: PASS\n- logsumexp: PASS\n- log_softmax: PASS\n- entropy: PASS\n- normalize: PASS\n- whiten: PASS\n- masked_whiten: PASS\n- masked_max: PASS\n- normalized_entropy: PASS\n\nKey conventions discovered:\n- `masked_mean` axis=None: 0.0 fallback on empty mask; axis=int uses `denom.clamp(min=1)` (0/1=0, no keepdim).\n- `masked_sum`: plain `(v*m).sum(dim=axis)`, no special empty handling.\n- `entropy` = masked_mean of per-position softmax entropy over last dim; returns scalar; 0.0 on all-zero mask.\n- `normalized_entropy` = entropy / log(vocab_size) where vocab = last dim; nan when vocab=1 (matches ref).\n- `normalize` = `(x-mean)/(std+eps)` with **unbiased** std.\n- `whiten`: uses **masked** mean and **biased** masked variance, `(v-mean)/sqrt(var+1e-8)`; when `shift_mean=False` adds mean back; denominator clamped to min=1 for empty mask (gives finite values, not nan).\n- `masked_whiten`: same as whiten but multiplies the whitened result by mask **before** the optional mean shift-back , so empty mask yields all zeros.\n- `masked_max`: global max over masked positions (fill unmasked with -inf); special-cases empty mask to 0.0.\n\nFull source of `/app/part1.py`:\n\n```python\nfrom __future__ import annotations\n\nimport math\n\nimport torch\n\n\ndef masked_mean(values, mask, axis=None):\n    if axis is None:\n        denom = mask.sum()\n        if denom == 0:\n            return torch.zeros((), dtype=values.dtype, device=values.device)\n        return (values * mask).sum() / denom\n    num = (values * mask).sum(dim=axis)\n    denom = mask.sum(dim=axis)\n    return num / denom.clamp(min=1)\n\n\ndef masked_sum(values, mask, axis=None):\n    if axis is None:\n        return (values * mask).sum()\n    return (values * mask).sum(dim=axis)\n\n\ndef logsumexp(x, axis):\n    return torch.logsumexp(x, dim=axis)\n\n\ndef log_softmax(x, axis):\n    return torch.log_softmax(x, dim=axis)\n\n\ndef entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom\n\n\ndef normalize(x, eps):\n    return (x - x.mean()) / (x.std() + eps)\n\n\ndef whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_whiten(values, mask, shift_mean):\n    denom = mask.sum().clamp(min=1)\n    mean = (values * mask).sum() / denom\n    var = (((values - mean) ** 2) * mask).sum() / denom\n    out = (values - mean) / torch.sqrt(var + 1e-8)\n    out = out * mask\n    if not shift_mean:\n        out = out + mean\n    return out\n\n\ndef masked_max(values, mask):\n    if mask.sum() == 0:\n        return torch.zeros((), dtype=values.dtype, device=values.device)\n    filled = values.masked_fill(mask == 0, float(\"-inf\"))\n    return filled.max()\n\n\ndef normalized_entropy(logits, mask):\n    logp = torch.log_softmax(logits, dim=-1)\n    p = logp.exp()\n    ent = -(p * logp).sum(dim=-1)\n    vocab = logits.shape[-1]\n    denom = mask.sum()\n    if denom == 0:\n        return torch.zeros((), dtype=ent.dtype, device=ent.device)\n    return (ent * mask).sum() / denom / math.log(vocab)\n```"}

{"type": "text", "text": "agentId: a8ab0e0c2a3fc9eb3 (use SendMessage with to: 'a8ab0e0c2a3fc9eb3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 37980\ntool_uses: 33\nduration_ms: 262016</usage>"}

{"type": "text", "text": "All 10 functions reverse-engineered and verified. Here is the final report.\n\n## Summary\n\nI reverse-engineered all 10 `reforacle` functions by probing with varied shapes, dtypes, signs, and edge cases, then verified each against the oracle with `compare()` at n≥300 (plus larger stress runs).\n\n### Per-function pass/fail (all PASS)\n```\ncumulative_max ...... PASS  (1D, 2D, int, single-elem)\nquantile_lower ...... PASS  (1D, 2D, q=0/1, single-row/col)\nmedian_reward ....... PASS  (1D, 2D, single)\nmode_label .......... PASS  (1D, 2D, ties, all-same, single)\nargmax_tokens ....... PASS  (1D, 2D, single-elem last dim)\nfirst_nonzero_index . PASS  (binary/frac/int/count masks, 1D+2D, all-zero)\npad_mask_from_lengths PASS  (normal, len>max_len, zeros)\nbucketize_reward .... PASS  (random, exact boundaries, empty boundaries)\ntop_k_mask .......... PASS  (1D, 2D, k>n, ties, k=0 raises)\ntop_p_mask .......... PASS  (1D, 2D, straddle, peaky, uniform)\n```\n\n### Key conventions discovered (the non-obvious ones)\n- **cumulative_max**: NOT a normal cummax. It is an *exclusive/shifted* cummax along dim 0: `out[0]=x[0]`, `out[i]=max(x[0..i-1])`. Returns values only (no tuple).\n- **quantile_lower / median_reward (2D)**: operate along dim 0 but in a peculiar way , they **sort each row**, then median/quantile is taken over rows *by original row index*. median = average of `sort(row[(n-1)//2])` and `sort(row[n//2])`; quantile_lower = `sort(row[floor(q*(n-1))])`. (1D uses plain `torch.quantile` with `interpolation='lower'`/`'linear'`.)\n- **mode_label**: most frequent label, ties broken to the **larger** value (opposite of `torch.mode`); per-row for 2D; scalar int64.\n- **first_nonzero_index**: implemented as the buggy idiom `argmax(mask.long() * arange(n,0,-1))` with a `sum(mask) <= 0 → -1` guard. For a true 0/1 mask this equals first-nonzero, but values are truncated-to-long and position-weighted, so it's only equivalent for proper masks. Per-row for 2D, -1 if a row sums to ≤0.\n- **bucketize_reward**: `torch.bucketize(..., right=True)`.\n- **top_k_mask**: returns a **bool** mask via threshold `logits >= kth-largest-value` (so ties can select >k elements); `k` clamped to `min(k, n)` (k>n → all True); `k=0` raises RuntimeError.\n- **top_p_mask**: returns **renormalized probabilities** (kept elements sum to 1, excluded set to 0), NOT a mask. Inclusion rule uses the *exclusive* cumsum of descending-sorted probs: keep where `cumsum_before_token < p`, always keeping the top-1.\n\nDeliverable written to `/app/part2.py` (standalone, imports only `torch`; the only \"reforacle\" mention is in a comment). Full source is shown above. `/app/objectives.py` was not modified."}

{"type": "text", "text": "agentId: ab8a55331340147b3 (use SendMessage with to: 'ab8a55331340147b3', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 138643\ntool_uses: 112\nduration_ms: 1361957</usage>"}
Agent
{
  "description": "Reverse-engineer composite objectives",
  "prompt": "You are reverse-engineering a sealed reference module `reforacle` (importable: `import reforacle`) to reproduce its EXACT numerical behavior in pure torch. You CANNOT read source; only call & compare.\n\nHelper: `from harness import compare` at /app/harness.py , `compare(ref_fn, cand_fn, make_inputs, n=200, atol=1e-5, rtol=1e-4)` (make_inputs returns tuple of args w/ fresh randoms). For these COMPOSITE objectives use atol=1e-5, rtol=1e-4. Use heavily.\n\nImplement these 5 composite functions EXACTLY. Each composes primitives , PROBE the composite directly to match, but here are the CONFIRMED conventions of reforacle's primitives (reforacle uses these internally, so replicate them):\n- token_logprobs(logits,labels) = log_softmax(logits,-1).gather(-1, labels.unsqueeze(-1)).squeeze(-1), shape = labels.shape.\n- masked_mean(v,m) = (v*m).sum()/m.sum(), returns 0 if m.sum()==0.\n- grpo_advantages(rewards, group_size, scale_by_std): flat=rewards.reshape(-1); groups=flat.reshape(-1,group_size); adv=groups-mean; if scale_by_std adv/=(std_biased+1e-6); returns adv.reshape(-1). Groups are CONTIGUOUS blocks of size group_size.\n- rloo_advantages(rewards, group_size): (group_size/(group_size-1))*(r-group_mean), flattened.\n- kl_penalty(logp,ref_logp,estimator): d=logp-ref_logp; k1=d; k2=0.5*d^2; k3=exp(-d)-1+d. (per-element)\n- clipped_pg_loss: ratio=exp(logp-old_logp); l1=ratio*adv; l2=clamp(ratio,1-clip_low,1+clip_high)*adv; loss = -masked_mean(min(l1,l2), mask).\n- sequence_logprob(logits,labels,mask,length_normalize): sum over seq of token_logprobs*mask; if length_normalize divide by mask.sum(-1).clamp(min=1).\n\nSignatures (keep EXACTLY):\n```\ndef dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,\n                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,\n                      beta, label_smoothing):\n    # Compute sequence logprobs: pc = sum(token_logprobs(pc_logits,chosen_labels)*chosen_mask) per batch (NOT length-normalized -- VERIFY), similarly pr, rc, rr. Then dpo_loss(pc,pr,rc,rr,beta,label_smoothing) = mean(-(1-ls)*logsigmoid(beta*((pc-rc)-(pr-rr))) - ls*logsigmoid(-...)). Returns scalar. PROBE whether seq logprob is length-normalized (likely NOT). shapes: *_logits (B,T,V), labels (B,T), mask (B,T).\n\ndef grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,\n                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,\n                   kl_estimator):\n    # Per-token logp=token_logprobs(logits,labels); old_logp, ref_logp similarly. advantages=grpo_advantages(rewards,group_size,scale_by_std) -> shape (B,), broadcast per token. pg = clipped surrogate per token: ratio=exp(logp-old_logp); min(ratio*adv, clamp(ratio,1-clip_low,1+clip_high)*adv). kl = kl_penalty(logp,ref_logp,kl_estimator) per token. per-token objective = -(pg - beta*kl)  [i.e. loss]. Reduce with masked_mean over completion_mask. Returns scalar. PROBE sign, whether advantage broadcasts as adv.unsqueeze(-1), whether it's loss = -(surrogate) + beta*kl, and reduction (single masked_mean over all tokens vs per-sequence-then-mean).\n\ndef ppo_objective(rewards, values, old_values, logp, old_logp, next_value,\n                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):\n    # advantages=gae(rewards,values,next_value,gamma,lam) [time axis=dim0]; returns=advantages+values. Maybe whiten advantages? PROBE. pg_loss=clipped_pg_loss(logp,old_logp,advantages,mask=ones,clip_low,clip_high). v_loss=value_loss(values,old_values,returns,vf_clip)=0.5*mean(max((v-ret)^2,(vclip-ret)^2)). total = pg_loss + vf_coef*v_loss. Returns scalar. PROBE whether advantages are whitened/normalized before pg, and whether there's a mask (probably no mask arg -> full mean).\n\ndef rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):\n    # like grpo but advantages=rloo_advantages(rewards,group_size), no KL, no ref. logp/old_logp=token_logprobs. clipped surrogate per token with adv broadcast; loss=-masked_mean(min(...), mask). Returns scalar. PROBE.\n\ndef reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):\n    # logp=token_logprobs(logits,labels); ref_logp=token_logprobs(ref_logits,labels). Per token: policy-gradient-ish term with advantages plus beta*reverse_kl term. reverse_kl per element = exp(-(logp-ref_logp))-1+(logp-ref_logp) (k3). Likely objective = -masked_mean(logp*advantages - beta*rkl, mask) OR masked_mean(advantages*logp) style. advantages shape: probably (B,) broadcast per token, or (B,T). PROBE carefully , determine exact form and sign.\n```\n\nCRITICAL: For each, print reforacle's output on fixed small inputs and reconstruct the formula by matching candidate implementations. Determine EXACTLY: sign of loss, whether advantages are broadcast with .unsqueeze(-1), whether reduction is one global masked_mean vs mean-over-sequences, whether advantages get whitened. Build candidates and use compare() at atol=1e-5, rtol=1e-4, n>=200, across varied shapes (B in {2,4,6}, T in {3,5}, V in {4,7}), group_size dividing B, and edge cases.\n\nDeliverables:\n1. Write /app/part6.py: `import torch` (+torch.nn.functional as F if needed) + the 5 pure-torch defs (NO reforacle import), standalone. It may re-define needed helpers inline (token_logprobs, grpo_advantages, etc.) as local logic.\n2. Verify all 5 with compare() to robust pass.\n3. Final message: FULL /app/part6.py source + per-function pass/fail line and the exact formula you settled on for each.\n\nDo not modify /app/objectives.py. Take your time; correctness over speed.",
  "subagent_type": "general-purpose"
}

, output, 
{"type": "text", "text": "All 5 composite functions reproduced exactly. `/app/part6.py` is written and standalone (no reforacle import).\n\n## Verification results (compare() at atol=1e-5, rtol=1e-4, n=300 + edge cases)\n\n- **dpo_sequence_loss**: PASS (300/300) + empty-mask edge PASS\n- **grpo_objective**: PASS (300/300) + empty-mask edge PASS\n- **ppo_objective**: PASS (300/300)\n- **rloo_objective**: PASS (300/300)\n- **reverse_kl_objective**: PASS (300/300) + empty-mask edge PASS\n\nRan across B∈{2,4,6}, T∈{3,5,8}, V∈{4,7}, all group_sizes dividing B, all KL estimators (k1/k2/k3), both scale_by_std flags, plus zero-mask edge cases.\n\n## Exact formulas settled on\n\n1. **dpo_sequence_loss**: seq logprob = `sum(token_logprobs(logits,labels)*mask)` over T , **NOT length-normalized** (verified: normalized variant gave a different value). Then `loss = mean(-(1-ls)*logsigmoid(z) - ls*logsigmoid(-z))` where `z = beta*((pc-rc)-(pr-rr))`.\n\n2. **grpo_objective**: adv = `grpo_advantages(rewards,gs,scale_by_std)` (biased std, +1e-6), **broadcast via `.unsqueeze(-1)`**. `pg = min(ratio*adv, clamp(ratio,1-cl,1+ch)*adv)`, `kl = kl_penalty(logp,ref_logp,est)`, per-token `obj = -(pg - beta*kl)`, reduced by a **single global `masked_mean` over all tokens** (not per-sequence-then-mean).\n\n3. **ppo_objective**: `adv = gae(...)`, `returns = adv+values` (returns computed **before** whitening). **Advantages ARE whitened**: `(adv-adv.mean())/(adv.std(unbiased=False)+1e-8)` (biased std, eps 1e-8). `pg_loss = clipped_pg_loss(logp,old_logp,adv,mask=ones,...)`, `v_loss = 0.5*mean(max((v-ret)^2, (old_v+clamp(v-old_v,±vf_clip)-ret)^2))`, `total = pg_loss + vf_coef*v_loss`. No mask arg → full mean.\n\n4. **rloo_objective**: adv = `(gs/(gs-1))*(r-group_mean)`, **`.unsqueeze(-1)`** broadcast. `loss = -masked_mean(min(ratio*adv, clamp(ratio,1-cl,1+ch)*adv), mask)`. No KL/ref.\n\n5. **reverse_kl_objective**: advantages are shape **(B,)** broadcast via **`.unsqueeze(-1)`** (verified: (B,T) advantages produce a different ref value). `d = logp-ref_logp`, `rkl = exp(-d)-1+d` (k3), `loss = -masked_mean(logp*adv - beta*rkl, mask)`.\n\nConfirmed primitive conventions used internally: whiten uses **biased** std; value_loss uses the `old_values + clamp(values-old_values, ±clip)` clipping form; masked_mean returns 0 when mask sums to 0."}

{"type": "text", "text": "agentId: a9d68e91eaadd3a89 (use SendMessage with to: 'a9d68e91eaadd3a89', summary: '<5-10 word recap>' to continue this agent)\n<usage>subagent_tokens: 29610\ntool_uses: 18\nduration_ms: 145934</usage>"}

Read remaining part files

shell
for f in part2 part3 part4 part6; do echo "=== $f ==="; cat $f.py; done
output
=== part2 ===
import torch


def cumulative_max(x):
    # Exclusive (shifted) cumulative max along dim 0.
    # out[0] = x[0]; out[i] = max(x[0..i-1]) for i >= 1.
    cm = torch.cummax(x, dim=0).values
    out = torch.empty_like(cm)
    out[0] = x[0]
    if out.shape[0] > 1:
        out[1:] = cm[:-1]
    return out


def quantile_lower(x, q):
    if x.dim() <= 1:
        return torch.quantile(x, q, dim=0, interpolation='lower')
    # 2D: sort each row, then take the 'lower' quantile row (by original row order).
    n = x.shape[0]
    idx = int((torch.tensor(q) * (n - 1)).floor().item())
    return torch.sort(x[idx]).values


def median_reward(rewards):
    if rewards.dim() <= 1:
        return torch.quantile(rewards, 0.5, dim=0, interpolation='linear')
    # 2D: sort the two middle rows (by original row order) and average them.
    n = rewards.shape[0]
    lo = (n - 1) // 2
    hi = n // 2
    a = torch.sort(rewards[lo]).values
    b = torch.sort(rewards[hi]).values
    return (a + b) / 2


def _mode_1d(row):
    vals, counts = torch.unique(row, return_counts=True)
    best = counts.max()
    tied = vals[counts == best]
    return tied.max()


def mode_label(labels):
    # Most frequent label; ties broken toward the LARGER label value.
    # Operates per-row for 2D input.
    if labels.dim() <= 1:
        return _mode_1d(labels)
    return torch.stack([_mode_1d(row) for row in labels])


def argmax_tokens(logits):
    return torch.argmax(logits, dim=-1)


def _first_nonzero_1d(row):
    # Reproduces reforacle's idiom: argmax(mask.long() * descending_positions),
    # with a sum <= 0 guard (on the original values) mapping to -1. For a proper
    # 0/1 mask this equals the true first-nonzero index.
    n = row.shape[0]
    if row.sum().item() <= 0:
        return -1
    w = torch.arange(n, 0, -1, device=row.device)
    return int(torch.argmax(row.long() * w).item())


def first_nonzero_index(mask):
    # Per-row for 2D; -1 if a row has no nonzero.
    if mask.dim() <= 1:
        return torch.tensor(_first_nonzero_1d(mask))
    return torch.tensor([_first_nonzero_1d(row) for row in mask])


def pad_mask_from_lengths(lengths, max_len):
    positions = torch.arange(max_len, device=lengths.device)
    mask = positions.unsqueeze(0) < lengths.unsqueeze(1)
    return mask.float()


def bucketize_reward(rewards, boundaries):
    return torch.bucketize(rewards, boundaries, right=True)


def top_k_mask(logits, k):
    kk = min(k, logits.shape[-1])
    vals = torch.topk(logits, kk, dim=-1).values
    thr = vals[..., -1:]
    return logits >= thr


def top_p_mask(probs, p):
    sp, si = torch.sort(probs, descending=True, dim=-1)
    cum = torch.cumsum(sp, dim=-1)
    excl = cum - sp  # exclusive cumulative sum
    keep_sorted = excl < p
    keep_sorted[..., 0] = True  # always keep the top-1 token
    keep = torch.zeros_like(keep_sorted)
    keep.scatter_(-1, si, keep_sorted)
    kept = probs * keep
    return kept / kept.sum(dim=-1, keepdim=True)
=== part3 ===
from __future__ import annotations

import torch
import torch.nn.functional as F


def selective_logprobs(logits, labels, mask):
    logp = F.log_softmax(logits, dim=-1)
    tok = logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    return (tok * mask).sum(-1)


def token_logprobs(logits, labels):
    logp = F.log_softmax(logits, dim=-1)
    return logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)


def sequence_logprob(logits, labels, mask, length_normalize):
    logp = F.log_softmax(logits, dim=-1)
    tok = logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    total = (tok * mask).sum(-1)
    if length_normalize:
        total = total / mask.sum(-1).clamp(min=1)
    return total


def smoothed_nll(logits, labels, smoothing):
    logp = F.log_softmax(logits, dim=-1)
    nll = -logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    smooth = -logp.mean(-1)
    loss = (1.0 - smoothing) * nll + smoothing * smooth
    return loss.mean()


def cross_entropy(logits, labels, ignore_index):
    logp = F.log_softmax(logits, dim=-1)
    safe = labels.clamp(min=0)
    nll = -logp.gather(-1, safe.unsqueeze(-1)).squeeze(-1)
    mask = (labels != ignore_index).to(nll.dtype)
    return (nll * mask).sum() / mask.sum().clamp(min=1)


def logprob_at_temperature(logits, labels, temperature):
    logp = F.log_softmax(logits / temperature, dim=-1)
    return logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
=== part4 ===
import torch


def grpo_advantages(rewards, group_size, scale_by_std):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    adv = groups - mean
    if scale_by_std:
        std = groups.std(dim=1, unbiased=False, keepdim=True)
        adv = adv / (std + 1e-6)
    return adv.reshape(-1)


def gae(rewards, values, next_value, gamma, lam):
    T = rewards.shape[0]
    advantages = torch.zeros_like(rewards)
    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)
    next_v = next_value
    for t in range(T - 1, -1, -1):
        delta = rewards[t] + gamma * next_v - values[t]
        last_adv = delta + gamma * lam * last_adv
        advantages[t] = last_adv
        next_v = values[t]
    return advantages


def discounted_returns(rewards, gamma):
    T = rewards.shape[0]
    returns = torch.zeros_like(rewards)
    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)
    for t in range(T - 1, -1, -1):
        acc = rewards[t] + gamma * acc
        returns[t] = acc
    return returns


def lambda_returns(rewards, values, next_value, gamma, lam):
    return gae(rewards, values, next_value, gamma, lam) + values


def rloo_advantages(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    adv = (group_size / (group_size - 1)) * (groups - mean)
    return adv.reshape(-1)


def group_mean_baseline(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    return (groups - mean).reshape(-1)


def advantage_mean_std(advantages, mask):
    w = mask
    wsum = w.sum()
    mean = (w * advantages).sum() / wsum
    var = (w * (advantages - mean) ** 2).sum() / wsum
    std = torch.sqrt(var)
    result = torch.stack([mean, std])
    result = torch.nan_to_num(result, nan=0.0)
    return result
=== part6 ===
import torch
import torch.nn.functional as F


def _token_logprobs(logits, labels):
    return F.log_softmax(logits, -1).gather(-1, labels.unsqueeze(-1)).squeeze(-1)


def _masked_mean(v, m):
    s = m.sum()
    if s.item() == 0:
        return torch.zeros((), dtype=v.dtype, device=v.device)
    return (v * m).sum() / s


def _grpo_advantages(rewards, group_size, scale_by_std):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(-1, keepdim=True)
    adv = groups - mean
    if scale_by_std:
        std = groups.std(unbiased=False, dim=-1, keepdim=True)
        adv = adv / (std + 1e-6)
    return adv.reshape(-1)


def _rloo_advantages(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(-1, keepdim=True)
    adv = (group_size / (group_size - 1)) * (groups - mean)
    return adv.reshape(-1)


def _gae(rewards, values, next_value, gamma, lam):
    T = rewards.shape[0]
    adv = torch.zeros_like(rewards)
    last = 0.0
    for t in reversed(range(T)):
        nv = next_value if t == T - 1 else values[t + 1]
        delta = rewards[t] + gamma * nv - values[t]
        last = delta + gamma * lam * last
        adv[t] = last
    return adv


def _kl_penalty(logp, ref_logp, estimator):
    d = logp - ref_logp
    if estimator == "k1":
        return d
    if estimator == "k2":
        return 0.5 * d * d
    # k3
    return torch.exp(-d) - 1 + d


def _clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * advantages
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages
    return -_masked_mean(torch.min(l1, l2), mask)


def _value_loss(values, old_values, returns, clip):
    vclipped = old_values + torch.clamp(values - old_values, -clip, clip)
    l1 = (values - returns) ** 2
    l2 = (vclipped - returns) ** 2
    return 0.5 * torch.max(l1, l2).mean()


def dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,
                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,
                      beta, label_smoothing):
    def seqlp(logits, labels, mask):
        return (_token_logprobs(logits, labels) * mask).sum(-1)
    pc = seqlp(pc_logits, chosen_labels, chosen_mask)
    pr = seqlp(pr_logits, rejected_labels, rejected_mask)
    rc = seqlp(rc_logits, chosen_labels, chosen_mask)
    rr = seqlp(rr_logits, rejected_labels, rejected_mask)
    logits = beta * ((pc - rc) - (pr - rr))
    ls = label_smoothing
    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)
    return loss.mean()


def grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,
                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,
                   kl_estimator):
    logp = _token_logprobs(logits, labels)
    old_logp = _token_logprobs(old_logits, labels)
    ref_logp = _token_logprobs(ref_logits, labels)
    adv = _grpo_advantages(rewards, group_size, scale_by_std).unsqueeze(-1)
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * adv
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * adv
    pg = torch.min(l1, l2)
    kl = _kl_penalty(logp, ref_logp, kl_estimator)
    obj = -(pg - beta * kl)
    return _masked_mean(obj, completion_mask)


def ppo_objective(rewards, values, old_values, logp, old_logp, next_value,
                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):
    adv = _gae(rewards, values, next_value, gamma, lam)
    returns = adv + values
    adv = (adv - adv.mean()) / (adv.std(unbiased=False) + 1e-8)
    mask = torch.ones_like(logp)
    pg_loss = _clipped_pg_loss(logp, old_logp, adv, mask, clip_low, clip_high)
    v_loss = _value_loss(values, old_values, returns, vf_clip)
    return pg_loss + vf_coef * v_loss


def rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):
    logp = _token_logprobs(logits, labels)
    old_logp = _token_logprobs(old_logits, labels)
    adv = _rloo_advantages(rewards, group_size).unsqueeze(-1)
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * adv
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * adv
    return -_masked_mean(torch.min(l1, l2), mask)


def reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):
    logp = _token_logprobs(logits, labels)
    ref_logp = _token_logprobs(ref_logits, labels)
    adv = advantages.unsqueeze(-1)
    d = logp - ref_logp
    rkl = torch.exp(-d) - 1 + d
    return -_masked_mean(logp * adv - beta * rkl, mask)

[stdout]
=== part2 ===
import torch


def cumulative_max(x):
    # Exclusive (shifted) cumulative max along dim 0.
    # out[0] = x[0]; out[i] = max(x[0..i-1]) for i >= 1.
    cm = torch.cummax(x, dim=0).values
    out = torch.empty_like(cm)
    out[0] = x[0]
    if out.shape[0] > 1:
        out[1:] = cm[:-1]
    return out


def quantile_lower(x, q):
    if x.dim() <= 1:
        return torch.quantile(x, q, dim=0, interpolation='lower')
    # 2D: sort each row, then take the 'lower' quantile row (by original row order).
    n = x.shape[0]
    idx = int((torch.tensor(q) * (n - 1)).floor().item())
    return torch.sort(x[idx]).values


def median_reward(rewards):
    if rewards.dim() <= 1:
        return torch.quantile(rewards, 0.5, dim=0, interpolation='linear')
    # 2D: sort the two middle rows (by original row order) and average them.
    n = rewards.shape[0]
    lo = (n - 1) // 2
    hi = n // 2
    a = torch.sort(rewards[lo]).values
    b = torch.sort(rewards[hi]).values
    return (a + b) / 2


def _mode_1d(row):
    vals, counts = torch.unique(row, return_counts=True)
    best = counts.max()
    tied = vals[counts == best]
    return tied.max()


def mode_label(labels):
    # Most frequent label; ties broken toward the LARGER label value.
    # Operates per-row for 2D input.
    if labels.dim() <= 1:
        return _mode_1d(labels)
    return torch.stack([_mode_1d(row) for row in labels])


def argmax_tokens(logits):
    return torch.argmax(logits, dim=-1)


def _first_nonzero_1d(row):
    # Reproduces reforacle's idiom: argmax(mask.long() * descending_positions),
    # with a sum <= 0 guard (on the original values) mapping to -1. For a proper
    # 0/1 mask this equals the true first-nonzero index.
    n = row.shape[0]
    if row.sum().item() <= 0:
        return -1
    w = torch.arange(n, 0, -1, device=row.device)
    return int(torch.argmax(row.long() * w).item())


def first_nonzero_index(mask):
    # Per-row for 2D; -1 if a row has no nonzero.
    if mask.dim() <= 1:
        return torch.tensor(_first_nonzero_1d(mask))
    return torch.tensor([_first_nonzero_1d(row) for row in mask])


def pad_mask_from_lengths(lengths, max_len):
    positions = torch.arange(max_len, device=lengths.device)
    mask = positions.unsqueeze(0) < lengths.unsqueeze(1)
    return mask.float()


def bucketize_reward(rewards, boundaries):
    return torch.bucketize(rewards, boundaries, right=True)


def top_k_mask(logits, k):
    kk = min(k, logits.shape[-1])
    vals = torch.topk(logits, kk, dim=-1).values
    thr = vals[..., -1:]
    return logits >= thr


def top_p_mask(probs, p):
    sp, si = torch.sort(probs, descending=True, dim=-1)
    cum = torch.cumsum(sp, dim=-1)
    excl = cum - sp  # exclusive cumulative sum
    keep_sorted = excl < p
    keep_sorted[..., 0] = True  # always keep the top-1 token
    keep = torch.zeros_like(keep_sorted)
    keep.scatter_(-1, si, keep_sorted)
    kept = probs * keep
    return kept / kept.sum(dim=-1, keepdim=True)
=== part3 ===
from __future__ import annotations

import torch
import torch.nn.functional as F


def selective_logprobs(logits, labels, mask):
    logp = F.log_softmax(logits, dim=-1)
    tok = logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    return (tok * mask).sum(-1)


def token_logprobs(logits, labels):
    logp = F.log_softmax(logits, dim=-1)
    return logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)


def sequence_logprob(logits, labels, mask, length_normalize):
    logp = F.log_softmax(logits, dim=-1)
    tok = logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    total = (tok * mask).sum(-1)
    if length_normalize:
        total = total / mask.sum(-1).clamp(min=1)
    return total


def smoothed_nll(logits, labels, smoothing):
    logp = F.log_softmax(logits, dim=-1)
    nll = -logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
    smooth = -logp.mean(-1)
    loss = (1.0 - smoothing) * nll + smoothing * smooth
    return loss.mean()


def cross_entropy(logits, labels, ignore_index):
    logp = F.log_softmax(logits, dim=-1)
    safe = labels.clamp(min=0)
    nll = -logp.gather(-1, safe.unsqueeze(-1)).squeeze(-1)
    mask = (labels != ignore_index).to(nll.dtype)
    return (nll * mask).sum() / mask.sum().clamp(min=1)


def logprob_at_temperature(logits, labels, temperature):
    logp = F.log_softmax(logits / temperature, dim=-1)
    return logp.gather(-1, labels.unsqueeze(-1)).squeeze(-1)
=== part4 ===
import torch


def grpo_advantages(rewards, group_size, scale_by_std):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    adv = groups - mean
    if scale_by_std:
        std = groups.std(dim=1, unbiased=False, keepdim=True)
        adv = adv / (std + 1e-6)
    return adv.reshape(-1)


def gae(rewards, values, next_value, gamma, lam):
    T = rewards.shape[0]
    advantages = torch.zeros_like(rewards)
    last_adv = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)
    next_v = next_value
    for t in range(T - 1, -1, -1):
        delta = rewards[t] + gamma * next_v - values[t]
        last_adv = delta + gamma * lam * last_adv
        advantages[t] = last_adv
        next_v = values[t]
    return advantages


def discounted_returns(rewards, gamma):
    T = rewards.shape[0]
    returns = torch.zeros_like(rewards)
    acc = torch.zeros(rewards.shape[1:], dtype=rewards.dtype, device=rewards.device)
    for t in range(T - 1, -1, -1):
        acc = rewards[t] + gamma * acc
        returns[t] = acc
    return returns


def lambda_returns(rewards, values, next_value, gamma, lam):
    return gae(rewards, values, next_value, gamma, lam) + values


def rloo_advantages(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    adv = (group_size / (group_size - 1)) * (groups - mean)
    return adv.reshape(-1)


def group_mean_baseline(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(dim=1, keepdim=True)
    return (groups - mean).reshape(-1)


def advantage_mean_std(advantages, mask):
    w = mask
    wsum = w.sum()
    mean = (w * advantages).sum() / wsum
    var = (w * (advantages - mean) ** 2).sum() / wsum
    std = torch.sqrt(var)
    result = torch.stack([mean, std])
    result = torch.nan_to_num(result, nan=0.0)
    return result
=== part6 ===
import torch
import torch.nn.functional as F


def _token_logprobs(logits, labels):
    return F.log_softmax(logits, -1).gather(-1, labels.unsqueeze(-1)).squeeze(-1)


def _masked_mean(v, m):
    s = m.sum()
    if s.item() == 0:
        return torch.zeros((), dtype=v.dtype, device=v.device)
    return (v * m).sum() / s


def _grpo_advantages(rewards, group_size, scale_by_std):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(-1, keepdim=True)
    adv = groups - mean
    if scale_by_std:
        std = groups.std(unbiased=False, dim=-1, keepdim=True)
        adv = adv / (std + 1e-6)
    return adv.reshape(-1)


def _rloo_advantages(rewards, group_size):
    flat = rewards.reshape(-1)
    groups = flat.reshape(-1, group_size)
    mean = groups.mean(-1, keepdim=True)
    adv = (group_size / (group_size - 1)) * (groups - mean)
    return adv.reshape(-1)


def _gae(rewards, values, next_value, gamma, lam):
    T = rewards.shape[0]
    adv = torch.zeros_like(rewards)
    last = 0.0
    for t in reversed(range(T)):
        nv = next_value if t == T - 1 else values[t + 1]
        delta = rewards[t] + gamma * nv - values[t]
        last = delta + gamma * lam * last
        adv[t] = last
    return adv


def _kl_penalty(logp, ref_logp, estimator):
    d = logp - ref_logp
    if estimator == "k1":
        return d
    if estimator == "k2":
        return 0.5 * d * d
    # k3
    return torch.exp(-d) - 1 + d


def _clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * advantages
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages
    return -_masked_mean(torch.min(l1, l2), mask)


def _value_loss(values, old_values, returns, clip):
    vclipped = old_values + torch.clamp(values - old_values, -clip, clip)
    l1 = (values - returns) ** 2
    l2 = (vclipped - returns) ** 2
    return 0.5 * torch.max(l1, l2).mean()


def dpo_sequence_loss(pc_logits, pr_logits, rc_logits, rr_logits,
                      chosen_labels, rejected_labels, chosen_mask, rejected_mask,
                      beta, label_smoothing):
    def seqlp(logits, labels, mask):
        return (_token_logprobs(logits, labels) * mask).sum(-1)
    pc = seqlp(pc_logits, chosen_labels, chosen_mask)
    pr = seqlp(pr_logits, rejected_labels, rejected_mask)
    rc = seqlp(rc_logits, chosen_labels, chosen_mask)
    rr = seqlp(rr_logits, rejected_labels, rejected_mask)
    logits = beta * ((pc - rc) - (pr - rr))
    ls = label_smoothing
    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)
    return loss.mean()


def grpo_objective(logits, old_logits, ref_logits, labels, completion_mask,
                   rewards, group_size, beta, clip_low, clip_high, scale_by_std,
                   kl_estimator):
    logp = _token_logprobs(logits, labels)
    old_logp = _token_logprobs(old_logits, labels)
    ref_logp = _token_logprobs(ref_logits, labels)
    adv = _grpo_advantages(rewards, group_size, scale_by_std).unsqueeze(-1)
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * adv
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * adv
    pg = torch.min(l1, l2)
    kl = _kl_penalty(logp, ref_logp, kl_estimator)
    obj = -(pg - beta * kl)
    return _masked_mean(obj, completion_mask)


def ppo_objective(rewards, values, old_values, logp, old_logp, next_value,
                  gamma, lam, clip_low, clip_high, vf_clip, vf_coef):
    adv = _gae(rewards, values, next_value, gamma, lam)
    returns = adv + values
    adv = (adv - adv.mean()) / (adv.std(unbiased=False) + 1e-8)
    mask = torch.ones_like(logp)
    pg_loss = _clipped_pg_loss(logp, old_logp, adv, mask, clip_low, clip_high)
    v_loss = _value_loss(values, old_values, returns, vf_clip)
    return pg_loss + vf_coef * v_loss


def rloo_objective(logits, old_logits, labels, mask, rewards, group_size, clip_low, clip_high):
    logp = _token_logprobs(logits, labels)
    old_logp = _token_logprobs(old_logits, labels)
    adv = _rloo_advantages(rewards, group_size).unsqueeze(-1)
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * adv
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * adv
    return -_masked_mean(torch.min(l1, l2), mask)


def reverse_kl_objective(logits, ref_logits, labels, mask, advantages, beta):
    logp = _token_logprobs(logits, labels)
    ref_logp = _token_logprobs(ref_logits, labels)
    adv = advantages.unsqueeze(-1)
    d = logp - ref_logp
    rkl = torch.exp(-d) - 1 + d
    return -_masked_mean(logp * adv - beta * rkl, mask)

Confirm part1 and part5 files

shell
ls -la /app/part*.py; echo "---part1---"; cat /app/part1.py; echo "---part5---"; cat /app/part5.py
output
-rw-r--r-- 1 root root 2172 Jul  1 05:09 /app/part1.py
-rw-r--r-- 1 root root 2974 Jul  1 05:27 /app/part2.py
-rw-r--r-- 1 root root 1411 Jul  1 05:08 /app/part3.py
-rw-r--r-- 1 root root 2002 Jul  1 05:08 /app/part4.py
-rw-r--r-- 1 root root 2009 Jul  1 05:08 /app/part5.py
-rw-r--r-- 1 root root 4601 Jul  1 05:30 /app/part6.py
---part1---
from __future__ import annotations

import math

import torch


def masked_mean(values, mask, axis=None):
    if axis is None:
        denom = mask.sum()
        if denom == 0:
            return torch.zeros((), dtype=values.dtype, device=values.device)
        return (values * mask).sum() / denom
    num = (values * mask).sum(dim=axis)
    denom = mask.sum(dim=axis)
    return num / denom.clamp(min=1)


def masked_sum(values, mask, axis=None):
    if axis is None:
        return (values * mask).sum()
    return (values * mask).sum(dim=axis)


def logsumexp(x, axis):
    return torch.logsumexp(x, dim=axis)


def log_softmax(x, axis):
    return torch.log_softmax(x, dim=axis)


def entropy(logits, mask):
    logp = torch.log_softmax(logits, dim=-1)
    p = logp.exp()
    ent = -(p * logp).sum(dim=-1)
    denom = mask.sum()
    if denom == 0:
        return torch.zeros((), dtype=ent.dtype, device=ent.device)
    return (ent * mask).sum() / denom


def normalize(x, eps):
    return (x - x.mean()) / (x.std() + eps)


def whiten(values, mask, shift_mean):
    denom = mask.sum().clamp(min=1)
    mean = (values * mask).sum() / denom
    var = (((values - mean) ** 2) * mask).sum() / denom
    out = (values - mean) / torch.sqrt(var + 1e-8)
    if not shift_mean:
        out = out + mean
    return out


def masked_whiten(values, mask, shift_mean):
    denom = mask.sum().clamp(min=1)
    mean = (values * mask).sum() / denom
    var = (((values - mean) ** 2) * mask).sum() / denom
    out = (values - mean) / torch.sqrt(var + 1e-8)
    out = out * mask
    if not shift_mean:
        out = out + mean
    return out


def masked_max(values, mask):
    if mask.sum() == 0:
        return torch.zeros((), dtype=values.dtype, device=values.device)
    filled = values.masked_fill(mask == 0, float("-inf"))
    return filled.max()


def normalized_entropy(logits, mask):
    logp = torch.log_softmax(logits, dim=-1)
    p = logp.exp()
    ent = -(p * logp).sum(dim=-1)
    vocab = logits.shape[-1]
    denom = mask.sum()
    if denom == 0:
        return torch.zeros((), dtype=ent.dtype, device=ent.device)
    return (ent * mask).sum() / denom / math.log(vocab)
---part5---
from __future__ import annotations

import torch
import torch.nn.functional as F


def dpo_loss(pc, pr, rc, rr, beta, label_smoothing):
    logits = beta * ((pc - rc) - (pr - rr))
    ls = label_smoothing
    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)
    return loss.mean()


def ipo_loss(pc, pr, rc, rr, beta):
    logits = (pc - rc) - (pr - rr)
    loss = (logits - 1.0 / (2.0 * beta)) ** 2
    return loss.mean()


def kl_penalty(logp, ref_logp, estimator):
    d = logp - ref_logp
    if estimator == "k1":
        return d
    if estimator == "k2":
        return 0.5 * d * d
    if estimator == "k3":
        return torch.exp(-d) - 1.0 + d
    raise ValueError(estimator)


def clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * advantages
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages
    m = torch.min(l1, l2)
    masked = (m * mask).sum() / mask.sum()
    return -masked


def value_loss(values, old_values, returns, clip):
    vclip = old_values + torch.clamp(values - old_values, -clip, clip)
    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()
    return loss


def reverse_kl(logp, ref_logp):
    d = logp - ref_logp
    return torch.exp(-d) - 1.0 + d


def symmetric_kl(logp, ref_logp):
    d = logp - ref_logp
    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0


def importance_ratio(logp, old_logp, clip):
    ratio = torch.exp(logp - old_logp)
    if clip is not None:
        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)
    return ratio


def bradley_terry_logit(chosen_reward, rejected_reward, beta):
    return beta * (chosen_reward - rejected_reward)


def huber_value_loss(values, returns, delta):
    return F.huber_loss(values, returns, delta=delta)


def clip_fraction(logp, old_logp, clip):
    ratio = torch.exp(logp - old_logp)
    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)
    return clipped.float().mean()

[stdout]
-rw-r--r-- 1 root root 2172 Jul  1 05:09 /app/part1.py
-rw-r--r-- 1 root root 2974 Jul  1 05:27 /app/part2.py
-rw-r--r-- 1 root root 1411 Jul  1 05:08 /app/part3.py
-rw-r--r-- 1 root root 2002 Jul  1 05:08 /app/part4.py
-rw-r--r-- 1 root root 2009 Jul  1 05:08 /app/part5.py
-rw-r--r-- 1 root root 4601 Jul  1 05:30 /app/part6.py
---part1---
from __future__ import annotations

import math

import torch


def masked_mean(values, mask, axis=None):
    if axis is None:
        denom = mask.sum()
        if denom == 0:
            return torch.zeros((), dtype=values.dtype, device=values.device)
        return (values * mask).sum() / denom
    num = (values * mask).sum(dim=axis)
    denom = mask.sum(dim=axis)
    return num / denom.clamp(min=1)


def masked_sum(values, mask, axis=None):
    if axis is None:
        return (values * mask).sum()
    return (values * mask).sum(dim=axis)


def logsumexp(x, axis):
    return torch.logsumexp(x, dim=axis)


def log_softmax(x, axis):
    return torch.log_softmax(x, dim=axis)


def entropy(logits, mask):
    logp = torch.log_softmax(logits, dim=-1)
    p = logp.exp()
    ent = -(p * logp).sum(dim=-1)
    denom = mask.sum()
    if denom == 0:
        return torch.zeros((), dtype=ent.dtype, device=ent.device)
    return (ent * mask).sum() / denom


def normalize(x, eps):
    return (x - x.mean()) / (x.std() + eps)


def whiten(values, mask, shift_mean):
    denom = mask.sum().clamp(min=1)
    mean = (values * mask).sum() / denom
    var = (((values - mean) ** 2) * mask).sum() / denom
    out = (values - mean) / torch.sqrt(var + 1e-8)
    if not shift_mean:
        out = out + mean
    return out


def masked_whiten(values, mask, shift_mean):
    denom = mask.sum().clamp(min=1)
    mean = (values * mask).sum() / denom
    var = (((values - mean) ** 2) * mask).sum() / denom
    out = (values - mean) / torch.sqrt(var + 1e-8)
    out = out * mask
    if not shift_mean:
        out = out + mean
    return out


def masked_max(values, mask):
    if mask.sum() == 0:
        return torch.zeros((), dtype=values.dtype, device=values.device)
    filled = values.masked_fill(mask == 0, float("-inf"))
    return filled.max()


def normalized_entropy(logits, mask):
    logp = torch.log_softmax(logits, dim=-1)
    p = logp.exp()
    ent = -(p * logp).sum(dim=-1)
    vocab = logits.shape[-1]
    denom = mask.sum()
    if denom == 0:
        return torch.zeros((), dtype=ent.dtype, device=ent.device)
    return (ent * mask).sum() / denom / math.log(vocab)
---part5---
from __future__ import annotations

import torch
import torch.nn.functional as F


def dpo_loss(pc, pr, rc, rr, beta, label_smoothing):
    logits = beta * ((pc - rc) - (pr - rr))
    ls = label_smoothing
    loss = -(1 - ls) * F.logsigmoid(logits) - ls * F.logsigmoid(-logits)
    return loss.mean()


def ipo_loss(pc, pr, rc, rr, beta):
    logits = (pc - rc) - (pr - rr)
    loss = (logits - 1.0 / (2.0 * beta)) ** 2
    return loss.mean()


def kl_penalty(logp, ref_logp, estimator):
    d = logp - ref_logp
    if estimator == "k1":
        return d
    if estimator == "k2":
        return 0.5 * d * d
    if estimator == "k3":
        return torch.exp(-d) - 1.0 + d
    raise ValueError(estimator)


def clipped_pg_loss(logp, old_logp, advantages, mask, clip_low, clip_high):
    ratio = torch.exp(logp - old_logp)
    l1 = ratio * advantages
    l2 = torch.clamp(ratio, 1 - clip_low, 1 + clip_high) * advantages
    m = torch.min(l1, l2)
    masked = (m * mask).sum() / mask.sum()
    return -masked


def value_loss(values, old_values, returns, clip):
    vclip = old_values + torch.clamp(values - old_values, -clip, clip)
    loss = 0.5 * torch.max((values - returns) ** 2, (vclip - returns) ** 2).mean()
    return loss


def reverse_kl(logp, ref_logp):
    d = logp - ref_logp
    return torch.exp(-d) - 1.0 + d


def symmetric_kl(logp, ref_logp):
    d = logp - ref_logp
    return 0.5 * (torch.exp(d) + torch.exp(-d)) - 1.0


def importance_ratio(logp, old_logp, clip):
    ratio = torch.exp(logp - old_logp)
    if clip is not None:
        ratio = torch.clamp(ratio, 1 - clip, 1 + clip)
    return ratio


def bradley_terry_logit(chosen_reward, rejected_reward, beta):
    return beta * (chosen_reward - rejected_reward)


def huber_value_loss(values, returns, delta):
    return F.huber_loss(values, returns, delta=delta)


def clip_fraction(logp, old_logp, clip):
    ratio = torch.exp(logp - old_logp)
    clipped = (ratio > 1 + clip) | (ratio < 1 - clip)
    return clipped.float().mean()

Assemble objectives.py from parts

shell
python3 - <<'EOF'
import re

header = '''from __future__ import annotations

import math

import torch
import torch.nn.functional as F


'''

bodies = []
for p in ['part1','part2','part3','part4','part5','part6']:
    src = open(f'{p}.py').read()
    # strip import lines and __future__
    lines = []
    for ln in src.splitlines():
        s = ln.strip()
        if s.startswith('from __future__') or s == 'import torch' or s == 'import math' or s.startswith('import torch.nn.functional'):
            continue
        lines.append(ln)
    body = '\n'.join(lines).strip('\n')
    bodies.append(f'# ===== {p} =====\n' + body)

out = header + '\n\n\n'.join(bodies) + '\n'
open('objectives.py','w').write(out)
print("written", len(out), "bytes")
EOF
python3 -c "import ast; ast.parse(open('/app/objectives.py').read()); print('syntax OK')"
output
written 15088 bytes
syntax OK

[stdout]
written 15088 bytes
syntax OK

Check all 49 functions present, no reforacle

shell
python3 - <<'EOF'
import ast
src=open('objectives.py').read()
assert 'reforacle' not in src, "reforacle referenced!"
tree=ast.parse(src)
defs=[n.name for n in tree.body if isinstance(n,ast.FunctionDef)]
stubs=[l.split('(')[0][4:] for l in open('/dev/stdin')] if False else None
import re
expected=re.findall(r'^def (\w+)\(', open('objectives.py.orig').read(),re.M) if False else None
# expected from original stub file content
orig="""masked_mean masked_sum logsumexp log_softmax selective_logprobs token_logprobs sequence_logprob entropy dpo_loss ipo_loss grpo_advantages gae kl_penalty clipped_pg_loss value_loss whiten dpo_sequence_loss grpo_objective ppo_objective rloo_advantages reverse_kl importance_ratio discounted_returns normalize top_p_mask smoothed_nll bradley_terry_logit rloo_objective reverse_kl_objective cross_entropy top_k_mask group_mean_baseline lambda_returns symmetric_kl huber_value_loss normalized_entropy clip_fraction masked_whiten logprob_at_temperature advantage_mean_std argmax_tokens mode_label median_reward masked_max quantile_lower pad_mask_from_lengths first_nonzero_index cumulative_max bucketize_reward""".split()
missing=[f for f in orig if f not in defs]
print("total defs:", len(defs), "expected 49 stubs +helpers")
print("MISSING:", missing)
print("only helpers extra:", [d for d in defs if d not in orig and not d.startswith('_')])
EOF
output
Exit code 1
Traceback (most recent call last):
  File "<stdin>", line 3, in <module>
AssertionError: reforacle referenced!

[error] tool reported failure

Find reforacle references

shell
grep -n reforacle /app/objectives.py
output
141:    # Reproduces reforacle's idiom: argmax(mask.long() * descending_positions),

[stdout]
141:    # Reproduces reforacle's idiom: argmax(mask.long() * descending_positions),

/app/objectives.py

− removed
    # Reproduces reforacle's idiom: argmax(mask.long() * descending_positions),
+ added
    # Idiom: argmax(mask.long() * descending_positions),

Strip reforacle from comments

shell
sed -i 's/reforacle/the reference/g' objectives.py && grep -n "reference\|reforacle" objectives.py
output
141:    # Reproduces the reference's idiom: argmax(mask.long() * descending_positions),

[stdout]
141:    # Reproduces the reference's idiom: argmax(mask.long() * descending_positions),

Verify function completeness

shell
python3 - <<'EOF'
import ast,re
src=open('objectives.py').read()
assert 'reforacle' not in src
defs=[n.name for n in ast.parse(src).body if isinstance(n,ast.FunctionDef)]
orig="masked_mean masked_sum logsumexp log_softmax selective_logprobs token_logprobs sequence_logprob entropy dpo_loss ipo_loss grpo_advantages gae kl_penalty clipped_pg_loss value_loss whiten dpo_sequence_loss grpo_objective ppo_objective rloo_advantages reverse_kl importance_ratio discounted_returns normalize top_p_mask smoothed_nll bradley_terry_logit rloo_objective reverse_kl_objective cross_entropy top_k_mask group_mean_baseline lambda_returns symmetric_kl huber_value_loss normalized_entropy clip_fraction masked_whiten logprob_at_temperature advantage_mean_std argmax_tokens mode_label median_reward masked_max quantile_lower pad_mask_from_lengths first_nonzero_index cumulative_max bucketize_reward".split()
print("missing:",[f for f in orig if f not in defs])
print("extra helpers:",[d for d in defs if d not in orig])
EOF
output
missing: []
extra helpers: ['_mode_1d', '_first_nonzero_1d', '_token_logprobs', '_masked_mean', '_grpo_advantages', '_rloo_advantages', '_gae', '_kl_penalty', '_clipped_pg_loss', '_value_loss']

[stdout]
missing: []
extra helpers: ['_mode_1d', '_first_nonzero_1d', '_token_logprobs', '_masked_mean', '_grpo_advantages', '_rloo_advantages', '_gae', '_kl_penalty', '_clipped_pg_loss', '_value_loss']
write · /app/verify_all.py
import torch, importlib
import reforacle as R
import objectives as O
from harness import compare

g = torch.Generator().manual_seed(12345)
def rn(*s): return torch.randn(*s, generator=g)
def ri(hi,*s): return torch.randint(0,hi,s,generator=g)
def rm(*s): return (torch.rand(*s, generator=g) > 0.4).float()

results = {}
def T(name, make, atol=1e-6, rtol=1e-5, n=250):
    ref=getattr(R,name); cand=getattr(O,name)
    ok=compare(ref,cand,make,n=n,atol=atol,rtol=rtol,verbose=False)
    results[name]=ok
    print(f"{'PASS' if ok else 'FAIL':4} {name}")
    if not ok:
        compare(ref,cand,make,n=5,atol=atol,rtol=rtol,verbose=True)

# --- primitives / reductions ---
T('masked_mean', lambda: (rn(3,5), rm(3,5), 1))
T('masked_mean', lambda: (rn(8), rm(8)))
T('masked_sum', lambda: (rn(4,6), rm(4,6), 0))
T('logsumexp', lambda: (rn(4,5), 1))
T('log_softmax', lambda: (rn(4,5), 1))
T('entropy', lambda: (rn(3,5,7), rm(3,5)))
T('normalize', lambda: (rn(9), 1e-5))
T('whiten', lambda: (rn(10), rm(10), bool(torch.rand(1,generator=g)>0.5)))
T('masked_whiten', lambda: (rn(10), rm(10), bool(torch.rand(1,generator=g)>0.5)))
T('masked_max', lambda: (rn(7), rm(7)))
T('normalized_entropy', lambda: (rn(3,5,7), rm(3,5)))

# --- misc primitives ---
T('cumulative_max', lambda: (rn(9),))
T('cumulative_max', lambda: (rn(6,4),))
T('quantile_lower', lambda: (rn(11), float(torch.rand(1,generator=g))))
T('median_reward', lambda: (rn(10),))
T('mode_label', lambda: (ri(5,12),))
T('mode_label', lambda: (ri(4,3,6),))
T('argmax_tokens', lambda: (rn(4,7),))
T('first_nonzero_index', lambda: (rm(9),))
T('first_nonzero_index', lambda: (rm(4,8),))
T('pad_mask_from_lengths', lambda: (torch.randint(0,7,(5,),generator=g), 7))
T('bucketize_reward', lambda: (rn(10), torch.sort(rn(4)).values))
T('top_k_mask', lambda: (rn(4,8), int(torch.randint(1,8,(1,),generator=g))))
T('top_p_mask', lambda: (torch.softmax(rn(4,8),-1), float(torch.rand(1,generator=g)*0.6+0.3)))

# --- logprobs ---
T('selective_logprobs', lambda: (rn(3,5,7), ri(7,3,5), rm(3,5)))
T('token_logprobs', lambda: (rn(3,5,7), ri(7,3,5)))
T('sequence_logprob', lambda: (rn(3,5,7), ri(7,3,5), rm(3,5), bool(torch.rand(1,generator=g)>0.5)))
T('smoothed_nll', lambda: (rn(3,5,7), ri(7,3,5), float(torch.rand(1,generator=g)*0.2)))
T('cross_entropy', lambda: (rn(6,7), ri(7,6), -100), 1e-6,1e-5)
T('cross_entropy', lambda: (rn(3,5,7), ri(7,3,5), -100))
T('logprob_at_temperature', lambda: (rn(3,5,7), ri(7,3,5), float(torch.rand(1,generator=g)*1.5+0.5)))

# --- advantages/returns ---
T('grpo_advantages', lambda: (rn(12), 4, bool(torch.rand(1,generator=g)>0.5)))
T('gae', lambda: (rn(6), rn(6), rn(()), 0.99, 0.95))
T('gae', lambda: (rn(6,3), rn(6,3), rn(3), 0.95, 0.9))
T('discounted_returns', lambda: (rn(7), 0.97))
T('discounted_returns', lambda: (rn(7,3), 0.9))
T('lambda_returns', lambda: (rn(6), rn(6), rn(()), 0.99, 0.95))
T('rloo_advantages', lambda: (rn(12), 4))
T('group_mean_baseline', lambda: (rn(15), 5))
T('advantage_mean_std', lambda: (rn(10), rm(10)))

# --- losses / KL ---
T('dpo_loss', lambda: (rn(8),rn(8),rn(8),rn(8), 0.1, float(torch.rand(1,generator=g)*0.2)))
T('ipo_loss', lambda: (rn(8),rn(8),rn(8),rn(8), 0.3))
for est in ['k1','k2','k3']:
    T(f'kl_penalty[{est}]', (lambda e: (lambda:(rn(9),rn(9),e)))(est)) if False else None
def mk_kl():
    est=['k1','k2','k3'][int(torch.randint(0,3,(1,),generator=g))]
    return (rn(9), rn(9), est)
T('kl_penalty', mk_kl)
T('clipped_pg_loss', lambda: (rn(4,5),rn(4,5),rn(4,5),rm(4,5),0.2,0.2))
T('value_loss', lambda: (rn(10),rn(10),rn(10),0.2))
T('reverse_kl', lambda: (rn(9),rn(9)))
T('symmetric_kl', lambda: (rn(9),rn(9)))
def mk_ir():
    clip=None if torch.rand(1,generator=g)>0.5 else 0.2
    return (rn(9),rn(9),clip)
T('importance_ratio', mk_ir)
T('bradley_terry_logit', lambda: (rn(8),rn(8),0.5))
T('huber_value_loss', lambda: (rn(10),rn(10), float(torch.rand(1,generator=g)*2+0.2)))
T('clip_fraction', lambda: (rn(20),rn(20),0.2))

# --- composite objectives (looser tol) ---
def mk_dpo_seq():
    B,Tt,V=4,5,7
    return (rn(B,Tt,V),rn(B,Tt,V),rn(B,Tt,V),rn(B,Tt,V),
            ri(V,B,Tt),ri(V,B,Tt),rm(B,Tt),rm(B,Tt),0.1,float(torch.rand(1,generator=g)*0.2))
T('dpo_sequence_loss', mk_dpo_seq, 1e-5,1e-4)
def mk_grpo():
    B,Tt,V=6,5,7
    est=['k1','k2','k3'][int(torch.randint(0,3,(1,),generator=g))]
    return (rn(B,Tt,V),rn(B,Tt,V),rn(B,Tt,V),ri(V,B,Tt),rm(B,Tt),
            rn(B),3,0.05,0.2,0.2,bool(torch.rand(1,generator=g)>0.5),est)
T('grpo_objective', mk_grpo, 1e-5,1e-4)
def mk_ppo():
    Tt=6
    return (rn(Tt),rn(Tt),rn(Tt),rn(Tt),rn(Tt),rn(()),0.99,0.95,0.2,0.2,0.2,0.5)
T('ppo_objective', mk_ppo, 1e-5,1e-4)
def mk_rloo():
    B,Tt,V=6,5,7
    return (rn(B,Tt,V),rn(B,Tt,V),ri(V,B,Tt),rm(B,Tt),rn(B),3,0.2,0.2)
T('rloo_objective', mk_rloo, 1e-5,1e-4)
def mk_rkl():
    B,Tt,V=4,5,7
    return (rn(B,Tt,V),rn(B,Tt,V),ri(V,B,Tt),rm(B,Tt),rn(B),0.1)
T('reverse_kl_objective', mk_rkl, 1e-5,1e-4)

print()
fails=[k for k,v in results.items() if not v]
print(f"TOTAL: {sum(results.values())}/{len(results)} pass. FAILS: {fails}")

Run comprehensive verification

shell
python3 verify_all.py 2>&1
output
PASS masked_mean
PASS masked_mean
PASS masked_sum
PASS logsumexp
PASS log_softmax
PASS entropy
PASS normalize
PASS whiten
PASS masked_whiten
PASS masked_max
PASS normalized_entropy
PASS cumulative_max
PASS cumulative_max
PASS quantile_lower
PASS median_reward
PASS mode_label
PASS mode_label
PASS argmax_tokens
PASS first_nonzero_index
PASS first_nonzero_index
PASS pad_mask_from_lengths
PASS bucketize_reward
PASS top_k_mask
PASS top_p_mask
PASS selective_logprobs
PASS token_logprobs
PASS sequence_logprob
PASS smoothed_nll
PASS cross_entropy
PASS cross_entropy
PASS logprob_at_temperature
PASS grpo_advantages
PASS gae
PASS gae
PASS discounted_returns
PASS discounted_returns
PASS lambda_returns
PASS rloo_advantages
PASS group_mean_baseline
PASS advantage_mean_std
PASS dpo_loss
PASS ipo_loss
PASS kl_penalty
PASS clipped_pg_loss
PASS value_loss
PASS reverse_kl
PASS symmetric_kl
PASS importance_ratio
PASS bradley_terry_logit
PASS huber_value_loss
PASS clip_fraction
PASS dpo_sequence_loss
PASS grpo_objective
PASS ppo_objective
PASS rloo_objective
PASS reverse_kl_objective

TOTAL: 49/49 pass. FAILS: []

[stdout]
PASS masked_mean
PASS masked_mean
PASS masked_sum
PASS logsumexp
PASS log_softmax
PASS entropy
PASS normalize
PASS whiten
PASS masked_whiten
PASS masked_max
PASS normalized_entropy
PASS cumulative_max
PASS cumulative_max
PASS quantile_lower
PASS median_reward
PASS mode_label
PASS mode_label
PASS argmax_tokens
PASS first_nonzero_index
PASS first_nonzero_index
PASS pad_mask_from_lengths
PASS bucketize_reward
PASS top_k_mask
PASS top_p_mask
PASS selective_logprobs
PASS token_logprobs
PASS sequence_logprob
PASS smoothed_nll
PASS cross_entropy
PASS cross_entropy
PASS logprob_at_temperature
PASS grpo_advantages
PASS gae
PASS gae
PASS discounted_returns
PASS discounted_returns
PASS lambda_returns
PASS rloo_advantages
PASS group_mean_baseline
PASS advantage_mean_std
PASS dpo_loss
PASS ipo_loss
PASS kl_penalty
PASS clipped_pg_loss
PASS value_loss
PASS reverse_kl
PASS symmetric_kl
PASS importance_ratio
PASS bradley_terry_logit
PASS huber_value_loss
PASS clip_fraction
PASS dpo_sequence_loss
PASS grpo_objective
PASS ppo_objective
PASS rloo_objective
PASS reverse_kl_objective

TOTAL: 49/49 pass. FAILS: []

Edge-case convention sweep

shell
python3 - <<'EOF'
import torch
import reforacle as R, objectives as O
g=torch.Generator().manual_seed(7)
def chk(name, r, c, atol=1e-5, rtol=1e-4):
    r=r if torch.is_tensor(r) else torch.tensor(float(r))
    c=c if torch.is_tensor(c) else torch.tensor(float(c))
    ok = r.shape==c.shape and torch.allclose(r.float(),c.float(),atol=atol,rtol=rtol,equal_nan=True)
    print(("OK  " if ok else "BAD "),name, "" if ok else f"ref={r.flatten()[:8].tolist()} got={c.flatten()[:8].tolist()}")

# cross_entropy with in-range ignore_index actually ignoring
for _ in range(3):
    lg=torch.randn(10,6,generator=g); lb=torch.randint(0,6,(10,),generator=g); ig=int(torch.randint(0,6,(1,),generator=g))
    chk(f"CE ignore={ig}", R.cross_entropy(lg,lb,ig), O.cross_entropy(lg,lb,ig),1e-6,1e-5)
# all ignored
lb=torch.full((8,),3); lg=torch.randn(8,6,generator=g)
chk("CE all-ignored", R.cross_entropy(lg,lb,3), O.cross_entropy(lg,lb,3),1e-6,1e-5)

# empty masks
z=torch.zeros(8)
chk("masked_mean empty", R.masked_mean(torch.randn(8,generator=g),z), O.masked_mean(torch.randn(8,generator=g),z),1e-6,1e-5)
chk("masked_max empty", R.masked_max(torch.randn(8,generator=g),z), O.masked_max(torch.randn(8,generator=g),z),1e-6,1e-5)
v=torch.randn(8,generator=g)
chk("whiten empty", R.whiten(v,z,True), O.whiten(v,z,True),1e-5,1e-4)
chk("masked_whiten empty", R.masked_whiten(v,z,False), O.masked_whiten(v,z,False),1e-5,1e-4)
adv=torch.randn(8,generator=g)
chk("adv_mean_std empty", R.advantage_mean_std(adv,z), O.advantage_mean_std(adv,z),1e-6,1e-5)

# entropy empty mask (2D)
lg=torch.randn(3,5,7,generator=g); m=torch.zeros(3,5)
chk("entropy empty", R.entropy(lg,m), O.entropy(lg,m),1e-6,1e-5)
chk("norm_entropy empty", R.normalized_entropy(lg,m), O.normalized_entropy(lg,m),1e-6,1e-5)

# quantile_lower 2D various q
for q in [0.0,0.1,0.25,0.5,0.75,0.9,1.0]:
    x=torch.randn(7,4,generator=g)
    chk(f"quantile2D q={q}", R.quantile_lower(x,q), O.quantile_lower(x,q),1e-6,1e-5)
    x1=torch.randn(9,generator=g)
    chk(f"quantile1D q={q}", R.quantile_lower(x1,q), O.quantile_lower(x1,q),1e-6,1e-5)

# median 2D odd/even
for n in [5,6,7,8]:
    x=torch.randn(n,3,generator=g)
    chk(f"median2D n={n}", R.median_reward(x), O.median_reward(x),1e-6,1e-5)

# bucketize with exact boundary values
b=torch.tensor([-1.0,0.0,1.0,2.0]); rw=torch.tensor([-1.0,0.0,0.5,1.0,2.0,3.0,-2.0])
chk("bucketize exact", R.bucketize_reward(rw,b), O.bucketize_reward(rw,b),0,0)

# mode ties
lb=torch.tensor([1,1,2,2,0]); chk("mode tie", R.mode_label(lb), O.mode_label(lb),0,0)
lb2=torch.tensor([[3,3,1,1],[0,2,2,0]]); chk("mode tie2d", R.mode_label(lb2), O.mode_label(lb2),0,0)

# first_nonzero all zero row
m=torch.tensor([[0.,0,0],[0,1,0]]); chk("fnz allzero", R.first_nonzero_index(m), O.first_nonzero_index(m),0,0)
m1=torch.zeros(5); chk("fnz allzero1d", R.first_nonzero_index(m1), O.first_nonzero_index(m1),0,0)

# pad_mask length>max_len and =0
L=torch.tensor([0,3,10,5]); chk("padmask", R.pad_mask_from_lengths(L,6), O.pad_mask_from_lengths(L,6),0,0)

# top_k k>n and k=n
lg=torch.randn(3,5,generator=g)
chk("topk k>n", R.top_k_mask(lg,9), O.top_k_mask(lg,9),0,0)
# top_p extremes
p=torch.softmax(torch.randn(3,6,generator=g),-1)
for pp in [0.01,0.5,0.99,1.0]:
    chk(f"topp p={pp}", R.top_p_mask(p,pp), O.top_p_mask(p,pp),1e-6,1e-5)

# sequence_logprob length_normalize with empty rows
lg=torch.randn(2,4,5,generator=g); lb=torch.randint(0,5,(2,4),generator=g); m=torch.zeros(2,4)
chk("seqlp empty norm", R.sequence_logprob(lg,lb,m,True), O.sequence_logprob(lg,lb,m,True),1e-6,1e-5)

# importance_ratio clip None
chk("ir None", R.importance_ratio(torch.randn(5,generator=g),torch.randn(5,generator=g),None),
    O.importance_ratio.__wrapped__ if False else O.importance_ratio(torch.randn(5,generator=g),torch.randn(5,generator=g),None))
EOF
output
OK   CE ignore=5 
OK   CE ignore=2 
OK   CE ignore=3 
OK   CE all-ignored 
OK   masked_mean empty 
OK   masked_max empty 
OK   whiten empty 
OK   masked_whiten empty 
OK   adv_mean_std empty 
OK   entropy empty 
OK   norm_entropy empty 
OK   quantile2D q=0.0 
OK   quantile1D q=0.0 
OK   quantile2D q=0.1 
OK   quantile1D q=0.1 
OK   quantile2D q=0.25 
OK   quantile1D q=0.25 
OK   quantile2D q=0.5 
OK   quantile1D q=0.5 
OK   quantile2D q=0.75 
OK   quantile1D q=0.75 
OK   quantile2D q=0.9 
OK   quantile1D q=0.9 
OK   quantile2D q=1.0 
OK   quantile1D q=1.0 
OK   median2D n=5 
OK   median2D n=6 
OK   median2D n=7 
OK   median2D n=8 
OK   bucketize exact 
OK   mode tie 
OK   mode tie2d 
OK   fnz allzero 
OK   fnz allzero1d 
OK   padmask 
OK   topk k>n 
OK   topp p=0.01 
OK   topp p=0.5 
OK   topp p=0.99 
OK   topp p=1.0 
OK   seqlp empty norm 
BAD  ir None ref=[1.6679655313491821, 10.705262184143066, 1.5934308767318726, 1.2461602687835693, 0.5517858266830444] got=[0.8851937055587769, 0.8908971548080444, 0.4740445911884308, 1.3474256992340088, 1.1427230834960938]

[stdout]
OK   CE ignore=5 
OK   CE ignore=2 
OK   CE ignore=3 
OK   CE all-ignored 
OK   masked_mean empty 
OK   masked_max empty 
OK   whiten empty 
OK   masked_whiten empty 
OK   adv_mean_std empty 
OK   entropy empty 
OK   norm_entropy empty 
OK   quantile2D q=0.0 
OK   quantile1D q=0.0 
OK   quantile2D q=0.1 
OK   quantile1D q=0.1 
OK   quantile2D q=0.25 
OK   quantile1D q=0.25 
OK   quantile2D q=0.5 
OK   quantile1D q=0.5 
OK   quantile2D q=0.75 
OK   quantile1D q=0.75 
OK   quantile2D q=0.9 
OK   quantile1D q=0.9 
OK   quantile2D q=1.0 
OK   quantile1D q=1.0 
OK   median2D n=5 
OK   median2D n=6 
OK   median2D n=7 
OK   median2D n=8 
OK   bucketize exact 
OK   mode tie 
OK   mode tie2d 
OK   fnz allzero 
OK   fnz allzero1d 
OK   padmask 
OK   topk k>n 
OK   topp p=0.01 
OK   topp p=0.5 
OK   topp p=0.99 
OK   topp p=1.0 
OK   seqlp empty norm 
BAD  ir None ref=[1.6679655313491821, 10.705262184143066, 1.5934308767318726, 1.2461602687835693, 0.5517858266830444] got=[0.8851937055587769, 0.8908971548080444, 0.4740445911884308, 1.3474256992340088, 1.1427230834960938]

Confirm importance_ratio and param sweeps

shell
python3 - <<'EOF'
import torch, reforacle as R, objectives as O
g=torch.Generator().manual_seed(3)
a=torch.randn(6,generator=g); b=torch.randn(6,generator=g)
print("None:", torch.allclose(R.importance_ratio(a,b,None), O.importance_ratio(a,b,None)))
print("0.2 :", torch.allclose(R.importance_ratio(a,b,0.2), O.importance_ratio(a,b,0.2)))
# also test dpo/ipo/value edge, huber various delta, clip_fraction boundary
for d in [0.1,0.5,1.0,2.0]:
    v=torch.randn(20,generator=g); r=torch.randn(20,generator=g)
    print(f"huber d={d}:", torch.allclose(R.huber_value_loss(v,r,d),O.huber_value_loss(v,r,d),atol=1e-6,rtol=1e-5))
# ipo different beta
for beta in [0.01,0.1,1.0]:
    a1,a2,a3,a4=[torch.randn(8,generator=g) for _ in range(4)]
    print(f"ipo b={beta}:", torch.allclose(R.ipo_loss(a1,a2,a3,a4,beta),O.ipo_loss(a1,a2,a3,a4,beta),atol=1e-5,rtol=1e-4))
EOF
output
None: True
0.2 : True
huber d=0.1: True
huber d=0.5: True
huber d=1.0: True
huber d=2.0: True
ipo b=0.01: True
ipo b=0.1: True
ipo b=1.0: True

[stdout]
None: True
0.2 : True
huber d=0.1: True
huber d=0.5: True
huber d=1.0: True
huber d=2.0: True
ipo b=0.01: True
ipo b=0.1: True
ipo b=1.0: True

Standalone import test in clean dir

shell
cd /tmp && cp /app/objectives.py /tmp/obj_standalone.py && python3 -c "
import sys
# simulate clean sandbox: ensure reforacle not importable path
import obj_standalone as O
print('imports OK, deps clean')
import inspect
print('functions:', sum(1 for n,f in inspect.getmembers(O,inspect.isfunction) if not n.startswith('_')))
" && bash /app/timer.sh
output
imports OK, deps clean
functions: 49
Remaining time (hours:minutes):
1:30
Shell cwd was reset to /app

[stdout]
imports OK, deps clean
functions: 49
Remaining time (hours:minutes):
1:30
[stderr]

Shell cwd was reset to /app

Final full-suite verification

shell
python3 verify_all.py 2>&1 | tail -3
output
PASS reverse_kl_objective

TOTAL: 49/49 pass. FAILS: []

[stdout]
PASS reverse_kl_objective

TOTAL: 49/49 pass. FAILS: []
All 49 functions are implemented and verified against `reforacle`. ## Summary I reimplemented all 49 functions in `/app/objectives.py` to reproduce the sealed `reforacle` module exactly, using only `torch` (plus `math`/`torch.nn.functional`) , no runtime dependency on the reference. **Approach:** Built a shared comparison harness (`harness.py`) that probes `reforacle` vs. a candidate across hundreds of random inputs (matching values *and* raised-exception types). Fanned out 6 parallel subagents, each owning a function group, to probe the reference and derive exact conventions, then assembled and independently re-verified the result. **Non-obvious conventions recovered by probing (not assumed):** - `masked_mean`/`entropy`/`masked_max` return **0**, not NaN, on empty masks; axis-reductions clamp the denominator. - `normalize` uses **unbiased** std; `whiten`/`masked_whiten`/`advantage_mean_std` use **biased** variance. - `cumulative_max` is an **exclusive/shifted** cummax (`out[i]=max(x[0..i-1])`). - `quantile_lower`/`median_reward` on 2D use a per-row-sort convention. - `mode_label` breaks ties toward the **larger** label. - `top_k_mask` returns a bool threshold mask; `top_p_mask` returns **renormalized probabilities** with an exclusive-cumsum inclusion rule. - `cross_entropy` clamps negatives before gather and returns **0** when all tokens are ignored (unlike `F.cross_entropy`). - `selective_logprobs` **sums over the sequence**; `sequence_logprob` normalizes with `clamp(min=1)`. - GAE/returns recurse along **dim 0** (time); `grpo_advantages` uses biased std + `1e-6` outside the sqrt; `rloo` uses the `n/(n-1)` factor. - `kl_penalty`/`reverse_kl`/`clip_fraction` sign/estimator conventions (`clip_fraction` uses separate `>`/`<` bound checks, diverging from `|ratio-1|>clip` at float boundaries). - Composite objectives: DPO seq-logprobs are **not** length-normalized; PPO **whitens advantages** (after computing returns); advantages broadcast via `.unsqueeze(-1)`. **Verification:** Full suite passes 49/49 at grading tolerances (primitives `atol=1e-6, rtol=1e-5`; composites `atol=1e-5, rtol=1e-4`), plus a dedicated edge-case sweep (in-range `ignore_index`, empty masks, boundary ties, `length>max_len`, tie-breaking, `clip=None`, extreme `top_p`). The file imports cleanly in a clean directory with no reference dependency. ~1h30 of budget remained.
Final diff , what the agent changed

No file changes, the agent left the workspace untouched.

Verifier output , the proof behind the reward
tests/test.sh
=== SyncVals verifier (post-training objectives, sealed oracle) ===

FUNCTIONS PASSED: 47/49  (partial_score=0.9592)
REWARD = 0   (1 iff ALL 49 functions match the sealed reference exactly)

The agent probes a sealed compiled oracle (reforacle) to recover 49 post-training objective conventions (DPO/IPO/GRPO/PPO/GAE/KL/RLOO) and reimplements them in torch.

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_a3515b6032e844b0. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_a3515b6032e844b0 · verifier authoritative; classifier explanatory.