EfficientNet-B0 — every parameter gradient node IS the loss's derivative in that parameter #

efficientnet_net_tiedG says each of the 262 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 and each block's cotangent its certified VJP's backward. enet_net_lossGrad composes them: 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 efficientnetForwardBFull with that one parameter varied. enet_net_lossGrad_smoothedCE discharges hL for the label-smoothed loss the artifacts ship.

How. MobileNetV2ParamGrad's shape:

• The tail every MBConv block shares (depthwise BN → swish → squeeze-excite → 1×1 project → project BN, over EnTail): the loss read at each of its activations and its gradient, the tie's own cotangent (enetTail_hasGradAt). Every stage VJP is global (swish has no kink), and the tie's cotangents are spelled as the certified backwards (bnBackB, swBackB, seInB), so each step is one HasGradAt.comp.
• The SE gate (enet_se_lossTiedB): with the block input dr held fixed, the SE output is the gated product dr ⊙ broadcast(σ(e2)) (seB_eq_gateMul), whose VJP in the gate is the emitted gateCotB (seGateMulBHasVJP). The loss read at the excite and reduce pre-activations then has the tie's cotE2 and cotE1 as its gradients, and the four SE dense nodes are its derivatives.
• Per block kind (at variable widths): the expand stage (stride 1 or at the input grid 2h × 2w) or none, the depthwise, then the tail. The stride-1 bundle serves both the skip blocks and the two widenings (b9, b16): a skip block's body sees the loss u ↦ Gn (u + v), whose gradient at the body output is still dyOut (enet_resid_lossTiedG).
• Bias nodes. B0 emits every conv and depthwise bias gradient with the BatchNorm β op (ConvBBetaTiedB); GradNodeB.biasBeta_hasGradAt makes it the bias gradient.
• Per net: the loss read after each block (enetSuf*), pulled back through the sixteen certified block VJPs and the head's, and each Φ identified with the whole net at updated weights by a standalone enet_factor_* theorem.

Hypotheses. B0Weights.EpsPos (every BN ε > 0), as in the tie; there is no smoothness hypothesis. For the smoothed loss, every example's target sums to one and 0 < nCls. Stochastic depth and classifier dropout are the tie's optional sites sd / cd here too (EfficientNetStepTieG's Scope): the loss is read at efficientnetForwardBFullDrop, a skip block's body sees the loss u ↦ Gn (dropPathOpt s u + v) whose gradient at the body output is dropPathOpt s dyOut (enet_resid_lossTiedG), the chain threads mbResidDropWHasVJP, and the head reads the dropped activation at the dense and pulls g back through the mask (headDoFwdBHasVJP).

Scope. One replica, at either precision: every conv and depthwise weight node is stated on the renderers' switch (convWeightGradBAt bf16 id …, depthwiseWeightGradBAt bf16 id …, …; Foundation.GradNodesBAt), so bf16 := true is the bf16 kind the efficientnetin*bf16 artifacts emit — efficientnetin_emarmsdp64dropdowxeps0001bf16, the book's ImageNet run, among them — read over ℝ at the identity rounding (Bf16Erasure), and bf16 := false the f32 artifacts'.