ViT-Tiny — every parameter gradient node IS the loss's derivative in that parameter #

vit_net_tiedGB says each of the 200 parameter gradient nodes denotes its layer's parameter Jacobian contracted with the cotangent the emitted backward chain threads to it, the chain's top being the smoothed-loss cotangent. vit_net_lossGrad composes that with the chain: for any loss L of the logits whose gradient at the net's output is g, every node is ∂L/∂θ of the WHOLE net vitNetB with that one parameter varied. vit_net_lossGrad_smoothedCE discharges hL for the label-smoothed loss the artifacts ship (smoothedBatchLossDiv, whose gradient is the softmaxDiv cotangent the render emits).

How. ConvNeXt's shape (ConvNeXtParamGrad.lean): no ViT op couples examples, so the work is per example and lifted once.

Per example (at variable widths): the loss read after each of a block's eight parameterised ops has the tie's own per-example cotangent as its gradient (vitPostL1_hasGradAt, vitPostQ_hasGradAt, …, vitPostF1_hasGradAt). Each is a short chain through certified VJPs: the MLP sublayer (mlpSubFlat_tie_v is its backward in the chain's spelling), the out-projection, the full attention layer for LN₁ (mhsaBackFlat_eq_mhsa_vjp).
The attention core in one of Q, K, V is the new piece. The render's per-head core is a column-slab map with a different function on each head's slab (head h reads K's and V's slab h), so colSlabApply generalises to colSlabApplyH and its Jacobian stays block-diagonal (pdivMat_colIndepH). Each head's VJP is the certified single-head sdpaBack{Q,K,V}, and the lifted backward IS the tie's coreQFlat / coreKFlat / coreVFlat (attnCoreQ_backward, …, all rfl).
Lifted (HasGradAt.pdiv_param_batchMap_through, ParamGrad): read against the linear loss ⟨·, dyₙ⟩ per example, those gradients turn each tied node's Σ_n Σ_j ∂per/∂θ · cotₙ into ∂G/∂θ of the batched block, G the loss at the block's output. Each node needs the block forward read as "the rest of the block ∘ the node's op ∘ the prefix" (vit_fwd_Wq, …), an equation up to Mat.unflatten_flatten.
Per net: the loss read after each stage (vitSuf*), pulled back through the certified batched block and head VJPs (vitBlockCotInB_eq_vjp, vitCotB2outB_eq_vjp), and each Φ identified with the whole net at updated weights by a standalone vit_factor_* theorem.

Two nodes are stated as in the tie. The classifier bias node biasGradB is the identity on its operand and the batch reduce is emitted text, so its statement is the sum over the batch of the node's per-example slices. The CLS token's node carries the batch sum inside den.

Hypotheses. 0 < ε (the LayerNorms' VJPs); no smoothness hypothesis (GELU has no kink). For the smoothed loss, every example's target sums to one and 0 < nC. Drop-path and the bf16 nodes are outside this statement, as they are outside the tie. Stated at ViT-Tiny's literal dims, as the tie is.

ViT-Tiny — every parameter gradient node IS the loss's derivative in that parameter #

The block forward, read after each node #

Differentiability #