Batched stride-1 conv weight GRADIENT denotes the certified Σ_n weight gradient. The un-fused peer of EnetFold.convWB_den: same Σ_n of conv_weight_grad_bridge, with no θ − lr· wrapper because the batched r34 render hands this node to an optimizer tail.

Batched stride-1 conv bias GRADIENT denotes the certified Σ_n bias gradient.

Batched strided conv weight GRADIENT denotes the certified Σ_n weight gradient. Generic in the kernel size, so the one lemma certifies the 7x7 stem AND every 3x3 downsample W1 AND every 1x1 projection Wp.

Batched strided conv bias GRADIENT denotes the certified Σ_n bias gradient.

Batched BN γ GRADIENT denotes the certified per-channel γ gradient over the merged batch+spatial axis m = N·(h·w). γ enters affinely, so there is no batch coupling in the PARAM gradient and this is bnPerChannelGradGamma_correct at that width, through the network→oc-major reindex bnchwFwd. Generic in the free β.

Batched BN β GRADIENT denotes the certified per-channel β gradient Σ_{batch,spatial} cot at m = N·(h·w). Carries a free v/γ — β's gradient is the channel sum and depends on neither.

Batched dense weight GRADIENT denotes the certified Σ_n outer product.

Batched dense bias GRADIENT denotes the certified Σ_n cotangent sum. r34's peer at a RECTANGULAR witness Mat a c, which the SE's c → r squeeze needs; the gradient is the channel sum and depends on neither W nor x, so the widening is free.

Batched XLA-SAME strided conv weight GRADIENT denotes the certified Σ_n weight gradient. B0's 3×3/s2 stem, the net's one XLA-phase site. Σ_n of flatConvStride2XlaWeightGradHasVJP.correct — the odd-phase weight VJP, so the certified gradient is the gradient of the net that ships.

Batched stride-1 depthwise weight GRADIENT denotes the certified Σ_n weight gradient. Σ_n of the flattened depthwiseWeightGradHasVJP3.correct. Generic in the kernel size, so the one lemma covers every 3×3 and every 5×5 depthwise.

Batched strided depthwise weight GRADIENT denotes the certified Σ_n weight gradient. The strided VJP is already flat, so this is Σ_n of depthwiseStride2WeightGradHasVJP.correct.

Batched XLA-SAME strided conv bias GRADIENT denotes the certified Σ_n bias gradient. The stem's bias slot, at convBias := true. Same reduce text as the stride-1 bias grad; the den is the odd-phase bias VJP.

Batched stride-1 depthwise bias GRADIENT denotes the certified Σ_n bias gradient. The depthwise bias slots at convBias := true. EfficientNet has no instance of this op — its depthwise convs are followed by BatchNorm, so their bias is always folded.

Batched XLA-SAME strided depthwise weight GRADIENT denotes the certified Σ_n weight gradient. The four stride-2 depthwises (b2/b4/b7/b14). Note: This is the Xla op — its weight-grad correlation keeps the [p−1, p+1] pad, the opposite asymmetry from the input-grad, and that asymmetry is the whole content of the variant. B0's strided depthwise is the SYMMETRIC op, so the two nets do not share this certificate.

Batched XLA-SAME strided depthwise bias GRADIENT denotes the certified Σ_n bias gradient. At convBias := true.

Batched patchify-stem weight GRADIENT denotes the certified Σ_n weight gradient. Note: The emitted convolution contracts the batch axis itself (the transpose trick), so the outer sum is inside one op rather than across N of them — same as the strided ops.

Batched vector-LN γ GRADIENT denotes the certified Σ_n γ gradient. Two levels: the outer sum is the batch, the inner one the tokens within one example. All 25 sites.

The SAME row-reduce op, certified against the vector-LN β forward. An LN β gradient and a dense bias gradient are the identical two-level reduce, so this constructor appears twice in the table against two different certified Jacobians — as it does per example. All 25 β sites.

Batched classifier weight GRADIENT denotes the certified Σ_n outer product.

Batched classifier bias GRADIENT denotes the certified cotangent, summed over the batch. The node's den carries the batch reduce its text prints, so this is the whole statement the classifier bias's update needs, as headWGradB_den is for the weight. a n is example n's head input (the bias gradient does not depend on it).