(θ', m', v') for one parameter under AdamW: the replica mean of its gradient (prettyAllReduceMean, pretty of the allReduceMeanF node) and then the proven adamMNextF/adamVNextF/adamWParamF triple (prettyAdamW).

(θ', b', s') for one parameter under RMSProp with momentum — the adamOne peer. Only ONE of the four ops is new. Reading the reference (jax/Jax/Codegen.lean, the .rmsprop branch) top to bottom:

⚠ The weight decay is COUPLED and goes FIRST, so the accumulator sees the decayed gradient. Reversing that order — decaying after the accumulator, AdamW-style — is a different optimizer and would not show up as an arity or type error anywhere.

⚠ EfficientNet's ε is 1e-3, where MobileNetV2's is 1.0 — the placement's sensitive end: at a collapsed mean-square the textbook spelling takes a step 31.6× larger (Proofs.rmsBufNext_eps_placement_at_zero). A green MobileNetV2 tie does not license the EfficientNet render; rms-tie efficientnet is its own gate.

Slot mapping: the packed [θ|m|v] signature is reused verbatim with m carrying the momentum buffer and v the running mean-square, the same slot reinterpretation the Nesterov render does for its velocity. That is why the driver and the interface do not move.

(θ', m', v', e') for one parameter under AdamW with the model-EMA shadow — ViT's and ConvNeXt's step. e' is "" at ema := false.

• wdName — "%wd", or the zero constant for timm's no_weight_decay parameters. The AdamW ops take the decay as an OPERAND NAME, so excluding a parameter binds that name to a zero.
• preAvg — the caller has ALREADY averaged (and clipped) this gradient, so the collective is not emitted a second time. Under data parallelism the clip must come AFTER the all_reduce (the reference clips the combined gradient; clipping per replica clips PARTIAL gradients — a different function that still trains and descends), and the clip needs every gradient at once while this step is per parameter, so at clip := true the caller hoists both (planning/archive/grad_clip.md §4).
• ema — the shadow e' = d·e + (1−d)·θ' is adamMNextF at (β₁ := d, m := e, g := θ'): Proofs.adamMNext IS the reference's ema_update (ema_update in jax/Jax/Codegen.lean), so it needs no new op and adamMNextF_faithful closes the den side by rfl. ⚠ It reads nT, the UPDATED parameter — the shadow averages weights after the optimizer moves them. ⚠ %emad/%oemad are function ARGS, not constants: the reference's decay is warmup-corrected, d = min(decay, (1+t)/(10+t)) (planning/archive/ema.md §2 — without it a shadow held 12.8% of the random init and scored 0.00%). At ema := false no pretty call happens, so the fresh-name counter does not move and the non-EMA renders are unchanged by the flag.

⚠ The shadow's SSA name is %{nm}e here; ResNet34RenderB.optOne uses %{nm}ema because at suffix e the stem BN gamma %sg collides with select_and_scatter's block-local %sge. ViT and ConvNeXt have no max-pool, so e is safe for them.

The packed train step's argument list after %x: the parameter regions in the order the driver packs them — θ, m, v, then the accumulator G (<p>a, only under gradient accumulation) and the model-EMA shadow E (<p>{emaSuf}, only under ema) — followed by the runtime scalars %lr, %bc1, %bc2, %aup, %akeep (accumulation) and %emad, %oemad (EMA). ps is (%name, type) per parameter, in signature order.

⚠ G precedes E and never follows it: [θ|m|v|G|E] is the order that leaves both single-axis layouts at the index they already occupy. ⚠ emaSuf is "e" except on the ResNet family, whose stem BN gamma %sg + e would be %sge — select_and_scatter's block-local name in the max-pool backward — so there it is "ema" (ResNet34RenderB.optOne).

The packed train step's leading result types, in packedTrainSig's order: the updated regions θ', m', v'[, G'][, E'], then %loss, %bc1, %bc2, then the handed-back accumulation / EMA scalars. pTy is the parameter types in signature order.

The stochastic-depth mask arguments , %dp<i>: tensor<Bxf32> for the sites idxs, in the order given — the order the driver's dropScales writes them into the blob. Empty when sd is off, which keeps every non-SD render byte-identical. Each net passes its own site list (vitDropSig, cnxDropSig, enetDropSig, r50DropSig).

conv, or its bf16 peer at rounding rnd when bf16.

convBackBatched, or its bf16 peer at rounding rnd when bf16.

convStride4, or its bf16 peer at rounding rnd when bf16.

convStride4WeightGradB, or its bf16 peer at rounding rnd when bf16.

convStrided, or its bf16 peer at rounding rnd when bf16.

convStridedBackBatched, or its bf16 peer at rounding rnd when bf16.

convStridedWeightGradB, or its bf16 peer at rounding rnd when bf16.

convStridedXla, or its bf16 peer at rounding rnd when bf16.

convStridedXlaWeightGradB, or its bf16 peer at rounding rnd when bf16.

convWeightGradB, or its bf16 peer at rounding rnd when bf16.

denseRow, or its bf16 peer at rounding rnd when bf16.

denseRowBack, or its bf16 peer at rounding rnd when bf16.

depthwise, or its bf16 peer at rounding rnd when bf16.

depthwiseBackBatched, or its bf16 peer at rounding rnd when bf16.

depthwiseStrided, or its bf16 peer at rounding rnd when bf16.

depthwiseStridedBackBatched, or its bf16 peer at rounding rnd when bf16.

depthwiseStridedWeightGradB, or its bf16 peer at rounding rnd when bf16.

depthwiseStridedXla, or its bf16 peer at rounding rnd when bf16.

depthwiseStridedXlaBackBatched, or its bf16 peer at rounding rnd when bf16.

depthwiseStridedXlaWeightGradB, or its bf16 peer at rounding rnd when bf16.

depthwiseWeightGradB, or its bf16 peer at rounding rnd when bf16.

flatConvF, or its bf16 peer at rounding rnd when bf16.

matmulFB, or its bf16 peer at rounding rnd when bf16.

rowDenseWeightGradB, or its bf16 peer at rounding rnd when bf16.

One frozen-statistic BN site at the per-example index — bnPerChannelEvalF on xin, with the running statistics arriving as graph inputs %{statP}mu / %{statP}var. The BN site of the per-example eval chains (r34FwdChain, r50FwdChain, mnv2FwdChain), which write @resnet34_fwd_eval, @resnet50in_fwd_eval and @mobilenetv2_fwd_eval: frozen-stat affine BN performs no reduction, so these forwards are class-batch-independent and partner the batch-BN train steps whose EMA'd μ/σ² they read. There is deliberately no training arm — the per-example training BN those chains once also emitted (bnPerChannelF) is not the BN any shipped train step uses.