worst-group-spurious-dfr

        TODO: implement the topological walk + seeding. (The per-op ``_backward`` closures do
        the local accumulation; here you only orchestrate the order + seed ``self.grad``.)
        """
        raise NotImplementedError("Tensor.backward")

        TODO: implement the topological walk + seeding. (The per-op ``_backward`` closures do
        the local accumulation; here you only orchestrate the order + seed ``self.grad``.)
        """
        topo: List[Tensor] = []
        visited = set()

        def build(node: "Tensor"):
            if id(node) in visited:
                return
            visited.add(id(node))
            for p in node._parents:
                build(p)
            topo.append(node)

        build(self)
        if grad is None:
            grad = np.ones_like(self.data)
        else:
            grad = _as_f64(grad)
        self._accum(grad)
        for node in reversed(topo):
            node._backward()

    def _bw():
        raise NotImplementedError("add backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(_unbroadcast(out.grad, a.data.shape))
        b._accum(_unbroadcast(out.grad, b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("sub backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(_unbroadcast(out.grad, a.data.shape))
        b._accum(_unbroadcast(-out.grad, b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("mul backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(_unbroadcast(out.grad * b.data, a.data.shape))
        b._accum(_unbroadcast(out.grad * a.data, b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("div backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(_unbroadcast(out.grad / b.data, a.data.shape))
        b._accum(_unbroadcast(-out.grad * a.data / (b.data * b.data), b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("power backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * pf * (a.data ** (pf - 1.0)))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("maximum backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        ad, bd = a.data, b.data
        ga = np.where(ad > bd, 1.0, np.where(ad == bd, 0.5, 0.0))
        a._accum(_unbroadcast(out.grad * ga, a.data.shape))
        b._accum(_unbroadcast(out.grad * (1.0 - ga), b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("minimum backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        ad, bd = a.data, b.data
        ga = np.where(ad < bd, 1.0, np.where(ad == bd, 0.5, 0.0))
        a._accum(_unbroadcast(out.grad * ga, a.data.shape))
        b._accum(_unbroadcast(out.grad * (1.0 - ga), b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("where backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(_unbroadcast(np.where(c, out.grad, 0.0), a.data.shape))
        b._accum(_unbroadcast(np.where(c, 0.0, out.grad), b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("exp backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * e)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("log backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad / a.data)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("sqrt backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * 0.5 / s)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("abs backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * np.sign(a.data))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("clip backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        mask = (a.data > lo) & (a.data < hi)
        a._accum(out.grad * mask)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("sum backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        a._accum(np.broadcast_to(g, a.data.shape).copy())
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("mean backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        a._accum(np.broadcast_to(g, a.data.shape) / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("max backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        mask = (a.data == m).astype(np.float64)
        cnt = mask.sum(axis=axis, keepdims=True)
        a._accum(np.broadcast_to(g, a.data.shape) * mask / cnt)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("min backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        mask = (a.data == m).astype(np.float64)
        cnt = mask.sum(axis=axis, keepdims=True)
        a._accum(np.broadcast_to(g, a.data.shape) * mask / cnt)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("transpose backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        if axes is None:
            a._accum(np.transpose(out.grad))
        else:
            inv = np.argsort(axes)
            a._accum(np.transpose(out.grad, tuple(inv)))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("reshape backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad.reshape(a.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("getitem backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        gz = np.zeros_like(a.data)
        np.add.at(gz, idx, out.grad)
        a._accum(gz)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("concat backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        splits = np.cumsum(sizes)[:-1]
        parts = np.split(out.grad, splits, axis=axis)
        for t, part in zip(ts, parts):
            t._accum(part)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("stack backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        parts = np.split(out.grad, len(ts), axis=axis)
        for i, t in enumerate(ts):
            t._accum(np.squeeze(parts[i], axis=axis))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("matmul backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        ga = g @ np.swapaxes(b.data, -1, -2)
        gb = np.swapaxes(a.data, -1, -2) @ g
        a._accum(_unbroadcast(ga, a.data.shape))
        b._accum(_unbroadcast(gb, b.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("relu backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * (a.data > 0.0))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("leaky_relu backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * np.where(a.data > 0.0, 1.0, sl))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("sigmoid backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * s * (1.0 - s))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("tanh backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * (1.0 - t * t))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("gelu backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        pdf = np.exp(-0.5 * x * x) / np.sqrt(2.0 * np.pi)
        a._accum(out.grad * (cdf + x * pdf))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("softmax backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        a._accum(s * (g - (g * s).sum(axis=axis, keepdims=True)))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("log_softmax backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        a._accum(g - s * g.sum(axis=axis, keepdims=True))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("softplus backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * (1.0 / (1.0 + np.exp(-bx))))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("silu backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * (sig + a.data * sig * (1.0 - sig)))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("elu backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * np.where(x > 0.0, 1.0, al * ex))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("mish backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        sig = 1.0 / (1.0 + np.exp(-x))
        a._accum(out.grad * (t + x * (1.0 - t * t) * sig))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("hardtanh backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        mask = (a.data > lo) & (a.data < hi)
        a._accum(out.grad * mask)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("var backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        m = n - ddof
        a._accum(np.broadcast_to(g, a.data.shape) * (2.0 / m) * (a.data - mu))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("std backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        if axis is not None and not keepdims:
            axes = (axis,) if isinstance(axis, int) else tuple(axis)
            axes = tuple(ax % a.data.ndim for ax in axes)
            g = np.expand_dims(g, axes)
        a._accum(np.broadcast_to(g, a.data.shape) * (a.data - mu) / (n * skeep))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("cumsum backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = out.grad
        flipped = np.flip(g, axis=axis)
        rev = np.cumsum(flipped, axis=axis)
        a._accum(np.flip(rev, axis=axis))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("mse_loss backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        pred._accum(out.grad * 2.0 * diff / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("cross_entropy backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * (sm - y) / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("group_weighted_ce backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * (sm - y) * scale[:, None])
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("reweighted_ce backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * (sm - y) * (w / wsum)[:, None])
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("group_dro_loss backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * (sm - y) * scale[:, None])
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("logit_adjusted_ce backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * (sm - y) / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("focal_loss backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        dfdp = g * ((1.0 - p) ** (g - 1.0)) * np.log(pc) - ((1.0 - p) ** g) / pc
        coef = dfdp * p / n            # (N,)
        logits._accum(out.grad * coef[:, None] * (y - sm))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("irm_penalty backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        sx = (sm * x).sum(axis=-1, keepdims=True)        # <s_i, x_i> (N,1)
        dgrad_w = (1.0 / n) * ((sm - y) + sm * (x - sx))  # d(grad_w)/d logit
        logits._accum(out.grad * 2.0 * grad_w * dgrad_w)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("gce_loss backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        coef = -(pc ** qf) / n            # (N,)
        logits._accum(out.grad * coef[:, None] * (y - sm))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("vrex_penalty backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        g = (2.0 / K) * (rd - mu)
        r._accum(out.grad * g.reshape(r.data.shape))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("ldam_loss backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        y = np.zeros_like(sm)
        y[np.arange(n), t] = 1.0
        logits._accum(out.grad * sc * (sm - y) / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("spectral_decoupling backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        logits._accum(out.grad * lm * x / n)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("layernorm backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad
        if beta.requires_grad:
            beta._accum(_unbroadcast(go, beta.data.shape))
        if gamma.requires_grad:
            gamma._accum(_unbroadcast(go * xhat, gamma.data.shape))
        if a.requires_grad:
            gxhat = go * gamma.data
            m1 = gxhat.mean(axis=-1, keepdims=True)
            m2 = (gxhat * xhat).mean(axis=-1, keepdims=True)
            a._accum(inv * (gxhat - m1 - xhat * m2))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("batchnorm backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad
        if beta.requires_grad:
            beta._accum(_unbroadcast(go, beta.data.shape))
        if gamma.requires_grad:
            gamma._accum(_unbroadcast(go * xhat, gamma.data.shape))
        if a.requires_grad:
            gxhat = go * gamma.data
            m1 = gxhat.mean(axis=0, keepdims=True)
            m2 = (gxhat * xhat).mean(axis=0, keepdims=True)
            a._accum(inv * (gxhat - m1 - xhat * m2))
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("batchnorm2d backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad
        ax = (0, 2, 3)
        if beta.requires_grad:
            beta._accum(go.sum(axis=ax))
        if gamma.requires_grad:
            gamma._accum((go * xhat).sum(axis=ax))
        if x.requires_grad:
            gxhat = go * gamma.data.reshape(1, C, 1, 1)
            if training:
                m1 = gxhat.mean(axis=ax, keepdims=True)
                m2 = (gxhat * xhat).mean(axis=ax, keepdims=True)
                x._accum(inv * (gxhat - m1 - xhat * m2))
            else:
                x._accum(gxhat * inv)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("rms_norm backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad
        if gamma.requires_grad:
            gamma._accum(_unbroadcast(go * xhat, gamma.data.shape))
        if a.requires_grad:
            gy = go * gamma.data
            s = (gy * x).sum(axis=-1, keepdims=True)
            a._accum(r * gy - (r ** 3 / D) * x * s)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("groupnorm2d backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad
        if beta.requires_grad:
            beta._accum(go.sum(axis=(0, 2, 3)))
        if gamma.requires_grad:
            gamma._accum((go * xhat).sum(axis=(0, 2, 3)))
        if x.requires_grad:
            gxhat = (go * g_).reshape(N, G, cg * H * W)
            xh = xhat.reshape(N, G, cg * H * W)
            m1 = gxhat.mean(axis=2, keepdims=True)
            m2 = (gxhat * xh).mean(axis=2, keepdims=True)
            dx = (inv * (gxhat - m1 - xh * m2)).reshape(N, C, H, W)
            x._accum(dx)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("conv2d backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad.reshape(N, Cout, OH * OW)
        if bias.requires_grad:
            bias._accum(go.sum(axis=(0, 2)))
        if weight.requires_grad:
            dWm = np.einsum("nop,nkp->ok", go, cols)
            weight._accum(dWm.reshape(weight.data.shape))
        if x.requires_grad:
            dcols = np.einsum("ok,nop->nkp", Wm, go)
            dcols = dcols.reshape(N, Cin, kh, kw, OH, OW)
            H, W = x.data.shape[2], x.data.shape[3]
            xp = np.zeros((N, Cin, H + 2 * pad, W + 2 * pad), np.float64)
            for i in range(kh):
                for j in range(kw):
                    xp[:, :, i:i + st * OH:st, j:j + st * OW:st] += dcols[:, :, i, j]
            if pad:
                dx = xp[:, :, pad:pad + H, pad:pad + W]
            else:
                dx = xp
            x._accum(dx)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("maxpool2d backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad[:, :, :, None, :, None]
        mask = (xr == outd[:, :, :, None, :, None]).astype(np.float64)
        cnt = mask.sum(axis=(3, 5), keepdims=True)
        dx = (mask * go / cnt).reshape(N, C, H, W)
        x._accum(dx)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("maxpool2d_stride backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad[:, :, None, None, :, :]
        mask = (win == outd[:, :, None, None, :, :]).astype(np.float64)
        cnt = mask.sum(axis=(2, 3), keepdims=True)
        dwin = mask * go / cnt
        gxp = np.zeros((N, C, Hp, Wp), np.float64)
        for i in range(k):
            for j in range(k):
                gxp[:, :, i:i + st * OH:st, j:j + st * OW:st] += dwin[:, :, i, j]
        if pad:
            dx = gxp[:, :, pad:pad + H, pad:pad + W]
        else:
            dx = gxp
        x._accum(dx)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("avgpool2d backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad[:, :, :, None, :, None]
        dx = np.broadcast_to(go / (k * k), (N, C, H // k, k, W // k, k)).reshape(N, C, H, W)
        x._accum(dx.copy())
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("global_avg_pool backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        go = out.grad[:, :, None, None]
        dx = np.broadcast_to(go / (H * W), (N, C, H, W)).copy()
        x._accum(dx)
    out._backward = _bw
    return out

    def _bw():
        raise NotImplementedError("embedding backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        gz = np.zeros_like(weight.data)
        np.add.at(gz, idx, out.grad)
        weight._accum(gz)
    out._backward = _bw
    return out

        def _bw_id():
            raise NotImplementedError("dropout backward")  # TODO
        out._backward = _bw_id
        return out

        def _bw_id():
            if out.grad is None:
                return
            a._accum(out.grad)
        out._backward = _bw_id
        return out

    def _bw():
        raise NotImplementedError("dropout backward")  # TODO
    out._backward = _bw
    return out

    def _bw():
        if out.grad is None:
            return
        a._accum(out.grad * keep)
    out._backward = _bw
    return out

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        d = {"weight": self.weight}

    def forward(self, x: Tensor) -> Tensor:
        y = ag.matmul(x, self.weight)
        if self.bias is not None:
            y = ag.add(y, self.bias)
        return y
    def named_params(self):
        d = {"weight": self.weight}

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {"weight": self.weight, "bias": self.bias}

    def forward(self, x: Tensor) -> Tensor:
        return ag.conv2d(x, self.weight, self.bias, pad=self.pad, stride=1)
    def named_params(self):
        return {"weight": self.weight, "bias": self.bias}

    def forward(self, x: Tensor, training: bool = True) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}

    def buffers(self):

    def forward(self, x: Tensor, training: bool = True) -> Tensor:
        return ag.batchnorm2d(x, self.gamma, self.beta, self.running_mean, self.running_var,
                              training=training, momentum=self.momentum, eps=self.eps)
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}

    def buffers(self):

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}


class LayerNorm(Module):

    def forward(self, x: Tensor) -> Tensor:
        return ag.batchnorm(x, self.gamma, self.beta, eps=self.eps)
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}


class LayerNorm(Module):

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}


class Dropout(Module):

    def forward(self, x: Tensor) -> Tensor:
        return ag.layernorm(x, self.gamma, self.beta, eps=self.eps)
    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}


class Dropout(Module):

    def forward(self, x: Tensor, training: bool = False, rng=None) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {}


class AvgPool2d(Module):

    def forward(self, x: Tensor, training: bool = False, rng=None) -> Tensor:
        return ag.dropout(x, self.p, training, rng)
    def named_params(self):
        return {}


class AvgPool2d(Module):

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {}


class MaxPool2d(Module):

    def forward(self, x: Tensor) -> Tensor:
        return ag.avgpool2d(x, self.k)
    def named_params(self):
        return {}


class MaxPool2d(Module):

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self):
        return {}


class RMSNorm(Module):

    def forward(self, x: Tensor) -> Tensor:
        return ag.maxpool2d(x, self.k)
    def named_params(self):
        return {}


class RMSNorm(Module):

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.rms_norm). See the docstring/contract.
        raise NotImplementedError("forward")

    def named_params(self):
        return {"gamma": self.gamma}

    def forward(self, x: Tensor) -> Tensor:
        return ag.rms_norm(x, self.gamma, eps=self.eps)

    def named_params(self):
        return {"gamma": self.gamma}

    def forward(self, x: Tensor) -> Tensor:
        # TODO: implement (compose ag.groupnorm2d). See the docstring/contract.
        raise NotImplementedError("forward")

    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}

    def forward(self, x: Tensor) -> Tensor:
        return ag.groupnorm2d(x, self.gamma, self.beta, self.num_groups, eps=self.eps)

    def named_params(self):
        return {"gamma": self.gamma, "beta": self.beta}

    def forward(self, X, training: bool = True) -> Tensor:
        # TODO: implement (stem->gn0->silu; then 2 residual blocks
        #   r=h; h=silu(b*n1(b*c1(h))); h=b*n2(b*c2(h)); h=silu(h + r);
        #   then strided downsample via ag.conv2d(h, down.weight, down.bias, pad=1, stride=2) + silu;
        #   then global-avg-pool over axes (2,3); then the linear head). Compose ag.* ops.
        raise NotImplementedError("forward")

    def forward(self, X, training: bool = True) -> Tensor:
        if not isinstance(X, Tensor):
            X = Tensor(X)
        h = ag.silu(self.gn0(self.stem(X)))
        # block 1
        r = h
        h = ag.silu(self.b1n1(self.b1c1(h)))
        h = self.b1n2(self.b1c2(h))
        h = ag.silu(ag.add(h, r))
        # block 2
        r = h
        h = ag.silu(self.b2n1(self.b2c1(h)))
        h = self.b2n2(self.b2c2(h))
        h = ag.silu(ag.add(h, r))
        # strided downsample
        h = ag.silu(ag.conv2d(h, self.down.weight, self.down.bias, pad=1, stride=2))
        h = ag.global_avg_pool(h)
        return self.head(h)

    def featurize(self, X, training: bool = True) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("featurize")
    def forward(self, X, training: bool = True) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")

    def featurize(self, X, training: bool = True) -> Tensor:
        if not isinstance(X, Tensor):
            X = Tensor(X)
        h = ag.relu(self.bn1(self.conv1(X), training=training))
        h = ag.maxpool2d(h, 2)
        h = ag.relu(self.bn2(self.conv2(h), training=training))
        h = ag.maxpool2d(h, 2)
        h = ag.relu(self.bn3(self.conv3(h), training=training))
        h = ag.global_avg_pool(h)
        h = ag.relu(self.embed(h))
        return h
    def forward(self, X, training: bool = True) -> Tensor:
        return self.classifier(self.featurize(X, training=training))

    def forward(self, x) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for i, lin in enumerate(self.layers):

    def forward(self, x) -> Tensor:
        if not isinstance(x, Tensor):
            x = Tensor(x)
        h = x
        for i, lin in enumerate(self.layers):
            h = lin(h)
            if i < len(self.layers) - 1:
                h = ag.relu(h)
        return h
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for i, lin in enumerate(self.layers):

    def forward(self, x) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for k, v in self.proj_in.named_params().items():
            d[f"proj_in.{k}"] = v

    def forward(self, x) -> Tensor:
        if not isinstance(x, Tensor):
            x = Tensor(x)
        h = self.proj_in(x)
        for blk in self.blocks:
            z = blk["ln"](h)
            z = ag.gelu(blk["fc1"](z))
            z = blk["fc2"](z)
            h = ag.add(h, z)
        return self.proj_out(h)
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for k, v in self.proj_in.named_params().items():
            d[f"proj_in.{k}"] = v

    def forward(self, X, training: bool = True) -> Tensor:
        # TODO: implement (compose ag.* ops). See the docstring/contract.
        raise NotImplementedError("forward")
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for name in ("conv1", "bn1", "conv2", "bn2", "head"):

    def forward(self, X, training: bool = True) -> Tensor:
        if not isinstance(X, Tensor):
            X = Tensor(X)
        h = ag.relu(self.bn1(self.conv1(X), training=training))
        h = ag.avgpool2d(h, 2)
        h = ag.relu(self.bn2(self.conv2(h), training=training))
        h = ag.maxpool2d(h, 2)
        N = h.shape[0]
        h = ag.reshape(h, (N, 2 * self.W * self.side * self.side))
        return self.head(h)
    def named_params(self) -> Dict[str, Tensor]:
        d: Dict[str, Tensor] = {}
        for name in ("conv1", "bn1", "conv2", "bn2", "head"):

    balanced-group / DFR weighting). If ``n_groups`` is None it is inferred as max(group_ids)+1."""
    # TODO: implement (numpy only). See docstring.
    raise NotImplementedError("balanced_group_weights")

    balanced-group / DFR weighting). If ``n_groups`` is None it is inferred as max(group_ids)+1."""
    gids = np.asarray(group_ids).astype(np.int64).reshape(-1)
    if n_groups is None:
        n_groups = int(gids.max()) + 1
    present = np.unique(gids)
    w = np.zeros(int(n_groups), dtype=np.float64)
    w[present] = 1.0 / len(present)
    return w

    effective number is (1-beta^n_c)/(1-beta) (Cui et al.); beta=0 reduces to inverse-frequency
    1/n_c. Each sample gets its class weight, and the vector is normalized to mean 1."""
    # TODO: implement (numpy only). See docstring.
    raise NotImplementedError("class_balanced_weights")

    effective number is (1-beta^n_c)/(1-beta) (Cui et al.); beta=0 reduces to inverse-frequency
    1/n_c. Each sample gets its class weight, and the vector is normalized to mean 1."""
    t = np.asarray(targets).astype(np.int64).reshape(-1)
    if n_classes is None:
        n_classes = int(t.max()) + 1
    counts = np.bincount(t, minlength=int(n_classes)).astype(np.float64)
    with np.errstate(divide="ignore", invalid="ignore"):
        if beta == 0.0:
            eff = counts
        else:
            eff = (1.0 - beta ** counts) / (1.0 - beta)
        raw = np.where(counts > 0, 1.0 / eff, 0.0)
    w = raw[t]
    w = w / w.mean()
    return w

    vector. Empty classes get log(eps)."""
    # TODO: implement (numpy only). See docstring.
    raise NotImplementedError("log_class_prior")

    vector. Empty classes get log(eps)."""
    t = np.asarray(targets).astype(np.int64).reshape(-1)
    if n_classes is None:
        n_classes = int(t.max()) + 1
    counts = np.bincount(t, minlength=int(n_classes)).astype(np.float64)
    N = counts.sum()
    prior = counts / N
    return np.where(counts > 0, np.log(np.where(prior > 0, prior, 1.0)), np.log(eps))

    Returns a length-``n_classes`` vector."""
    # TODO: implement (numpy only). See docstring.
    raise NotImplementedError("ldam_margins")

    Returns a length-``n_classes`` vector."""
    t = np.asarray(targets).astype(np.int64).reshape(-1)
    if n_classes is None:
        n_classes = int(t.max()) + 1
    counts = np.bincount(t, minlength=int(n_classes)).astype(np.float64)
    with np.errstate(divide="ignore", invalid="ignore"):
        m = np.where(counts > 0, counts ** (-0.25), 0.0)
    mx = m.max()
    if mx > 0:
        m = m * (max_margin / mx)
    return m

    the PRESENT classes. Returns a length-``n_classes`` per-CLASS weight vector (NOT per-sample)."""
    # TODO: implement (numpy only). See docstring.
    raise NotImplementedError("effective_number_weights")

    the PRESENT classes. Returns a length-``n_classes`` per-CLASS weight vector (NOT per-sample)."""
    t = np.asarray(targets).astype(np.int64).reshape(-1)
    if n_classes is None:
        n_classes = int(t.max()) + 1
    counts = np.bincount(t, minlength=int(n_classes)).astype(np.float64)
    present = counts > 0
    with np.errstate(divide="ignore", invalid="ignore"):
        eff = (1.0 - beta ** counts) / (1.0 - beta)
        w = np.where(present, 1.0 / eff, 0.0)
    mean_present = w[present].mean()
    if mean_present > 0:
        w = w / mean_present
    return w

    def update(self, group_losses, present=None):
        # TODO: implement the masked EMA update (see docstring). Return self.l.copy().
        raise NotImplementedError("EMAGroupLoss.update")

    def worst_group(self):
        # TODO: implement (argmax of the current EMA). See docstring.
        raise NotImplementedError("EMAGroupLoss.worst_group")

    def update(self, group_losses, present=None):
        gl = np.asarray(group_losses, dtype=np.float64).reshape(-1)
        if present is None:
            mask = np.ones(self.n_groups, dtype=bool)
        else:
            mask = np.asarray(present, dtype=bool).reshape(-1)
        for k in range(self.n_groups):
            if not mask[k]:
                continue
            if not self._init[k]:
                self.l[k] = gl[k]
                self._init[k] = True
            else:
                self.l[k] = self.beta * self.l[k] + (1.0 - self.beta) * gl[k]
        return self.l.copy()

    def worst_group(self):
        return int(np.argmax(self.l))

    def update(self, group_losses):
        # TODO: exponentiated-gradient update of self.q on group_losses; renormalize.
        raise NotImplementedError("GroupDROState.update")

    def update(self, group_losses):
        gl = np.asarray(group_losses, dtype=np.float64).reshape(-1)
        self.q = self.q * np.exp(self.eta_q * gl)
        self.q = self.q / self.q.sum()
        return self.q.copy()

    def step(self):
        # TODO: implement the SGD update (see module docstring). Update p.data in place.
        raise NotImplementedError("SGD.step")

    def step(self):
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            v = self.momentum * self._v[i] + g
            self._v[i] = v
            upd = (g + self.momentum * v) if self.nesterov else v
            p.data -= self.lr * upd

    def step(self):
        # TODO: implement the Adagrad update (see module docstring). Update p.data in place.
        raise NotImplementedError("Adagrad.step")

    def step(self):
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._s[i] = self._s[i] + g * g
            p.data -= self.lr * g / (np.sqrt(self._s[i]) + self.eps)

    def step(self):
        # TODO: implement the RMSprop update (see module docstring). Update p.data in place.
        raise NotImplementedError("RMSprop.step")

    def step(self):
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._s[i] = self.alpha * self._s[i] + (1 - self.alpha) * (g * g)
            p.data -= self.lr * g / (np.sqrt(self._s[i]) + self.eps)

    def step(self):
        # TODO: implement the Adam update (see module docstring). Update p.data in place.
        raise NotImplementedError("Adam.step")

    def step(self):
        self.t += 1
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._m[i] = self.b1 * self._m[i] + (1 - self.b1) * g
            self._v[i] = self.b2 * self._v[i] + (1 - self.b2) * (g * g)
            mhat = self._m[i] / (1 - self.b1 ** self.t)
            vhat = self._v[i] / (1 - self.b2 ** self.t)
            p.data -= self.lr * mhat / (np.sqrt(vhat) + self.eps)

    def step(self):
        # TODO: implement the AdamW update (see module docstring). Update p.data in place.
        raise NotImplementedError("AdamW.step")

    def step(self):
        self.t += 1
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad
            self._m[i] = self.b1 * self._m[i] + (1 - self.b1) * g
            self._v[i] = self.b2 * self._v[i] + (1 - self.b2) * (g * g)
            mhat = self._m[i] / (1 - self.b1 ** self.t)
            vhat = self._v[i] / (1 - self.b2 ** self.t)
            p.data -= self.lr * (mhat / (np.sqrt(vhat) + self.eps) + self.weight_decay * p.data)

    def step(self):
        # TODO: implement the Adamax update (see module docstring). Update p.data in place.
        raise NotImplementedError("Adamax.step")

    def step(self):
        self.t += 1
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._m[i] = self.b1 * self._m[i] + (1 - self.b1) * g
            self._u[i] = np.maximum(self.b2 * self._u[i], np.abs(g))
            p.data -= (self.lr / (1 - self.b1 ** self.t)) * self._m[i] / (self._u[i] + self.eps)

    def step(self):
        # TODO: implement the NAdam update (see module docstring). Update p.data in place.
        raise NotImplementedError("NAdam.step")

    def step(self):
        self.t += 1
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._m[i] = self.b1 * self._m[i] + (1 - self.b1) * g
            self._v[i] = self.b2 * self._v[i] + (1 - self.b2) * (g * g)
            mhat = self._m[i] / (1 - self.b1 ** self.t)
            vhat = self._v[i] / (1 - self.b2 ** self.t)
            mnes = self.b1 * mhat + (1 - self.b1) * g / (1 - self.b1 ** self.t)
            p.data -= self.lr * mnes / (np.sqrt(vhat) + self.eps)

    def step(self):
        # TODO: implement the Lion update (see module docstring). Update p.data in place.
        raise NotImplementedError("Lion.step")

    def step(self):
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad
            upd = np.sign(self.b1 * self._m[i] + (1 - self.b1) * g)
            p.data -= self.lr * (upd + self.weight_decay * p.data)
            self._m[i] = self.b2 * self._m[i] + (1 - self.b2) * g

    def step(self):
        # TODO: implement the RAdam update (see module docstring). Update p.data in place.
        raise NotImplementedError("RAdam.step")

    def step(self):
        self.t += 1
        t = self.t
        b1, b2 = self.b1, self.b2
        rinf = 2.0 / (1 - b2) - 1
        rt = rinf - 2 * t * (b2 ** t) / (1 - b2 ** t)
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad + self.weight_decay * p.data
            self._m[i] = b1 * self._m[i] + (1 - b1) * g
            self._v[i] = b2 * self._v[i] + (1 - b2) * (g * g)
            mhat = self._m[i] / (1 - b1 ** t)
            if rt > 4:
                l = np.sqrt((1 - b2 ** t) / (self._v[i] + self.eps))
                r = math.sqrt(((rt - 4) * (rt - 2) * rinf) / ((rinf - 4) * (rinf - 2) * rt))
                p.data -= self.lr * mhat * r * l
            else:
                p.data -= self.lr * mhat

    def step(self):
        # TODO: implement the AdaBelief update (see module docstring). Update p.data in place.
        raise NotImplementedError("AdaBelief.step")

    def step(self):
        self.t += 1
        for i, p in enumerate(self.params):
            if p.grad is None:
                continue
            g = p.grad
            self._m[i] = self.b1 * self._m[i] + (1 - self.b1) * g
            d = g - self._m[i]
            self._s[i] = self.b2 * self._s[i] + (1 - self.b2) * (d * d) + self.eps
            mhat = self._m[i] / (1 - self.b1 ** self.t)
            shat = self._s[i] / (1 - self.b2 ** self.t)
            p.data -= self.lr * (mhat / (np.sqrt(shat) + self.eps) + self.weight_decay * p.data)

    exceeds ``max_norm`` every grad is scaled by ``max_norm / (total_norm + 1e-6)``."""
    # TODO: implement (see docstring).
    raise NotImplementedError("clip_grad_norm")

    exceeds ``max_norm`` every grad is scaled by ``max_norm / (total_norm + 1e-6)``."""
    total = 0.0
    for p in params:
        if p.grad is not None:
            total += float((p.grad ** 2).sum())
    total = math.sqrt(total)
    if total > max_norm:
        scale = max_norm / (total + 1e-6)
        for p in params:
            if p.grad is not None:
                p.grad = p.grad * scale
    return total

    """Element-wise gradient clamp to [-clip_value, clip_value] (in place)."""
    # TODO: implement (see docstring).
    raise NotImplementedError("clip_grad_value")

    """Element-wise gradient clamp to [-clip_value, clip_value] (in place)."""
    for p in params:
        if p.grad is not None:
            p.grad = np.clip(p.grad, -clip_value, clip_value)

    ``total``. ``step`` is 0-based. Holds at ``min_lr`` past ``total``."""
    # TODO: implement (see docstring).
    raise NotImplementedError("cosine_lr")

    ``total``. ``step`` is 0-based. Holds at ``min_lr`` past ``total``."""
    if warmup > 0 and step < warmup:
        return base_lr * (step + 1) / warmup
    prog = min(1.0, max(0.0, (step - warmup) / max(1, total - warmup)))
    return min_lr + 0.5 * (base_lr - min_lr) * (1 + math.cos(math.pi * prog))

    """Linear warmup to ``base_lr`` over ``warmup`` steps, then constant ``base_lr``."""
    # TODO: implement (see docstring).
    raise NotImplementedError("warmup_lr")

    """Linear warmup to ``base_lr`` over ``warmup`` steps, then constant ``base_lr``."""
    if step < warmup:
        return base_lr * (step + 1) / warmup
    return base_lr

    """Step decay: lr = base_lr * gamma ** (step // step_size)."""
    # TODO: implement (see docstring).
    raise NotImplementedError("step_lr")

    """Step decay: lr = base_lr * gamma ** (step // step_size)."""
    return base_lr * gamma ** (step // step_size)

    """Exponential decay: lr = base_lr * gamma ** step."""
    # TODO: implement (see docstring).
    raise NotImplementedError("exponential_lr")

    """Exponential decay: lr = base_lr * gamma ** step."""
    return base_lr * gamma ** step

    ``step >= total`` holds at ``min_lr``. ``step`` is 0-based."""
    # TODO: implement (see docstring).
    raise NotImplementedError("polynomial_lr")

    ``step >= total`` holds at ``min_lr``. ``step`` is 0-based."""
    if step >= total:
        return min_lr
    return (base_lr - min_lr) * ((1 - step / total) ** power) + min_lr

    in-cycle step s: lr = min_lr + 0.5*(base_lr-min_lr)*(1+cos(pi*s/T)). ``step`` is 0-based."""
    # TODO: implement (see docstring).
    raise NotImplementedError("cosine_restart_lr")

    in-cycle step s: lr = min_lr + 0.5*(base_lr-min_lr)*(1+cos(pi*s/T)). ``step`` is 0-based."""
    s = step
    T = period
    while s >= T:
        s -= T
        T *= t_mult
    return min_lr + 0.5 * (base_lr - min_lr) * (1 + math.cos(math.pi * s / max(1, T)))

    """Flatten (y, g) to a single group id y*n_classes + g (int64)."""
    # TODO
    raise NotImplementedError("group_ids")

    """Flatten (y, g) to a single group id y*n_classes + g (int64)."""
    return (np.asarray(y, dtype=np.int64) * n_classes + np.asarray(g, dtype=np.int64)).astype(np.int64)

    """Yield (Xb, yb, gb) minibatches over a random permutation of the dataset."""
    # TODO
    raise NotImplementedError("iterate")

    """Yield (Xb, yb, gb) minibatches over a random permutation of the dataset."""
    n = len(y)
    perm = rng.permutation(n)
    for start in range(0, n, batch_size):
        idx = perm[start:start + batch_size]
        yield X[idx], y[idx], g[idx]

    """Return (min over (y,g) groups of within-group accuracy, average accuracy, per-group dict)."""
    # TODO
    raise NotImplementedError("worst_group_acc")

    """Return (min over (y,g) groups of within-group accuracy, average accuracy, per-group dict)."""
    preds = np.asarray(preds).reshape(-1)
    y = np.asarray(y).reshape(-1)
    g = np.asarray(g).reshape(-1)
    gid = group_ids(y, g, n_classes)
    correct = (preds == y).astype(np.float64)
    avg = float(correct.mean())
    per = {}
    for k in np.unique(gid):
        mask = gid == k
        per[int(k)] = float(correct[mask].mean())
    wga = min(per.values()) if per else 0.0
    return wga, avg, per

    """Boolean mask selecting ~frac of EACH (y,g) group (keeps both slices group-balanced)."""
    # TODO
    raise NotImplementedError("stratified_group_split")

    """Boolean mask selecting ~frac of EACH (y,g) group (keeps both slices group-balanced)."""
    y = np.asarray(y).reshape(-1)
    g = np.asarray(g).reshape(-1)
    gid = group_ids(y, g, n_classes)
    mask = np.zeros(len(y), dtype=bool)
    for k in np.unique(gid):
        idx = np.where(gid == k)[0]
        rng.shuffle(idx)
        ntake = int(round(frac * len(idx)))
        ntake = max(0, min(len(idx), ntake))
        mask[idx[:ntake]] = True
    return mask

    # TODO: build a SmallCNN(n_classes, img_size, width=WIDTH, embed_dim=EMBED_DIM), train a
    #       worst-group-robust recipe with your framework (forward -> loss -> backward -> clip ->
    #       optimizer step), then save:
    #           save_checkpoint(args.out, model.state_dict(), n_classes, img_size)
    raise NotImplementedError("implement training and call save_checkpoint")

    rng = np.random.default_rng(args.seed)

    Xtr, ytr, gtr = D.load_npz(args.train)
    Xrw, yrw, grw = D.load_npz(args.reweight)
    n_classes = int(max(ytr.max(), yrw.max())) + 1
    img_size = Xtr.shape[-1]
    print(f"n_classes={n_classes} img_size={img_size} train={Xtr.shape} reweight={Xrw.shape}")

    model = SmallCNN(n_classes=n_classes, img_size=img_size, width=WIDTH,
                     embed_dim=EMBED_DIM, seed=args.seed)

    # ---- Phase 1: ERM training of the full network (feature extractor) on the correlated split.
    feat_params = model.params()
    opt = O.AdamW(feat_params, lr=2e-3, weight_decay=1e-4)
    n_epochs = 25
    bs = 128
    n = len(ytr)
    nsteps = n_epochs * ((n + bs - 1) // bs)
    step = 0
    for ep in range(n_epochs):
        for Xb, yb, gb in D.iterate(Xtr, ytr, gtr, bs, rng):
            opt.lr = O.cosine_lr(step, nsteps, 2e-3, warmup=nsteps // 20, min_lr=1e-4)
            logits = model(Xb, training=True)
            loss = ag.cross_entropy(logits, yb)
            opt.zero_grad()
            loss.backward()
            O.clip_grad_norm(feat_params, 5.0)
            opt.step()
            step += 1
        # quick train acc
        if ep % 5 == 4 or ep == n_epochs - 1:
            preds = predict(model, Xtr, n_classes)
            acc = (preds == ytr).mean()
            print(f"[erm] epoch {ep+1}/{n_epochs} loss={float(loss.data):.4f} train_acc={acc:.3f}")

    # ---- Phase 2: DFR -- freeze extractor, re-fit ONLY the classifier on th
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