Cotangent at the project CONV's output — dyOut through the project BN's backward. ⭐ dyOut itself is the cotangent at the project BN's output: the bottleneck is linear, so nothing masks it. Feeds %u{p}pW.

Cotangent at the post-DW BN's output — the project conv's input-VJP, masked by the post-DW relu. Feeds %u{p}dg and %u{p}dbt.

Cotangent at the post-DW CONV's output — through the post-DW BN's backward. Feeds %u{p}dW.

Cotangent at the expand BN's output — masked by the expand relu. Feeds %u{p}eg/%u{p}ebt.

⭐⭐ This is where the chain DISPATCHES on the table, exactly as mnv4PostDWSlot does and off the same row: with a post-depthwise the incoming cotangent is that depthwise's input-VJP; without one (postDWk = 0, the ConvNeXt-like and FFN rows) the project conv's input-VJP arrives here directly, because the render emits no post-DW nodes at all. One chain, three stride-1 profiles, and the if reduces at every concrete row.

Cotangent at the expand CONV's output — through the expand BN's backward. Feeds %u{p}eW.

Cotangent at the pre-DW BN's output — the expand conv's input-VJP, masked by the pre-DW relu. Feeds %u{p}qg and %u{p}qbt.

Cotangent at the pre-DW CONV's output — through the pre-DW BN's backward. Feeds %u{p}qW.

Cotangent at the project CONV's output — dyOut through the project BN's backward. ⭐ dyOut itself is the cotangent at the project BN's output: the bottleneck is linear, so nothing masks it. Feeds %u{p}pW.

Cotangent at the post-DW BN's output — the project conv's input-VJP, masked by the post-DW relu. Feeds %u{p}dg and %u{p}dbt.

Cotangent at the post-DW CONV's output — through the post-DW BN's backward. Feeds %u{p}dW.

Cotangent at the expand BN's output — masked by the expand relu. Feeds %u{p}eg/%u{p}ebt.

⚠ No dispatch here, unlike the stride-1 chain: all three of Conv-M's stride-2 rows have postDWk > 0, so the post-depthwise is always present on this path.

Cotangent at the expand CONV's output — through the expand BN's backward. Feeds %u{p}eW.

Cotangent at the STRIDED pre-DW BN's output — the expand conv's input-VJP, masked by the pre-DW relu. Feeds %u{p}qg and %u{p}qbt.

Cotangent at the STRIDED pre-DW conv's output — through the pre-DW BN's backward. Feeds %u{p}qW.

The pre-strided block's input cotangent — the STRIDED depthwise's input-VJP, landing at 2h. No fan-in: ic ≠ oc, so the block has no skip.

The BODY's input cotangent — what the render's dx carries before the skip fan-in.

⭐ Dispatches on s.preDWk the way mnv4PreDWSlot does: with a pre-depthwise the body's dx is that depthwise's input-VJP, without one it is the expand conv's.

The skip fan-in itself: body dx + dyOut, at the block-input shape.

⚠ Split from mnv4BodyCotIn for the same reason mnv4SkipGraphB is split from the body graph builders: the add needs s.oc and s.ic to be the SAME type, which they are at every stride-1 row and are not at a row binder. The body's cotangent is row-generic; the add is applied at the concrete row, where s.oc = s.ic is rfl.

⭐ ExtraDW block, tied. All twelve parameter nodes — four conv/depthwise weights and four BatchNorm γ/β pairs — denote the certified batched Σ_n gradient at the real forward activations and the real backward-chain cotangent driven by dyOut.

⚠ Each BatchNorm's γ/β reads the cotangent at THAT BatchNorm's output (CotQn, CotEn, CotDn, and dyOut itself for the project) while its conv reads the one at the conv's output (CotQc, CotEc, CotDc, CotPc). Off by one and the gradient is silently wrong — the two have the same type. ⭐ The project BN's pair reads dyOut UNMASKED: the bottleneck is linear.

⛔ There are no conv-bias conjuncts: MobileNetV4RenderB has no convBias flag, so those ops are never emitted and every slot here is exercised by the artifact.

⭐ Pre-strided block, tied — rows 1, 3 and 11. All twelve parameter nodes — four conv/depthwise weights and four BatchNorm γ/β pairs — denote the certified batched Σ_n gradient at the real forward activations and the real backward-chain cotangent driven by dyOut.

⚠ Each BatchNorm's γ/β reads the cotangent at THAT BatchNorm's output (CotQn, CotEn, CotDn, and dyOut itself for the project) while its conv reads the one at the conv's output (CotQc, CotEc, CotDc, CotPc). Off by one and the gradient is silently wrong — the two have the same type. ⭐ The project BN's pair reads dyOut UNMASKED: the bottleneck is linear.

⚠⚠ The leading node is depthwiseStridedWeightGradB — depthwiseStride2Flat, SYMMETRIC padding, reading its input at 2h. Every other node is the stride-1 profile's at the reduced resolution, because the stride is consumed entirely by that first depthwise.

⛔ No skip and no addVB: ic ≠ oc at all three rows, so the block IS its body.

Cotangent at the stem BN's output — the fused stage's dx, masked by the stem relu. Feeds %sg and %sbt.

Cotangent at the stem CONV's output — through the stem BN's backward. Feeds %sW.

Stem, tied. Its three nodes at the chain's cotangents.

⛔⛔ And the chain STOPS here. There is no convStridedXlaBackBatched node: no render emits a gradient into %x, so the artifact's backward ends at this weight gradient. That is why the stem sits outside MobileNetV4FullB.lean's CertLayer trunk, and it is B0's situation exactly.

Cotangent at the fused stage's project CONV output. ⭐ dyF reaches the project BN's γ/β unmasked — the fused stage ends in a BatchNorm with no activation. Feeds %f0pW.

Cotangent at the fused BN's output — the project conv's input-VJP through swish's backward. ⭐ No mask: swish is smooth, which is why this stage carries no kink hypothesis anywhere. Feeds %f0cg and %f0cbt.

Cotangent at the fused CONV's output — through the fused BN's backward. Feeds %f0cW.

The fused stage's input cotangent — the SYMMETRIC strided conv's input-VJP, landing at 2h.

⭐ Fused stage, tied — its six parameter nodes. ⚠ %f0cW is convStridedWeightGradB, SYMMETRIC padding, where the stem's is the XLA-SAME twin: two phases in one net. ⭐ And the fused BN's γ/β read the cotangent that came through SWISH's backward, not through a relu mask — this is the one stage in MNv4 with no kink anywhere.

Cotangent at the SECOND head BN's output — the GAP/dense tail's input cotangent, masked by that stage's relu. Feeds %hg and %hbt.

Cotangent at the second head CONV's output. Feeds %hW.

Cotangent at the FIRST head BN's output. Feeds %h1g and %h1bt.

Cotangent at the first head CONV's output. Feeds %h1W.

The head's input cotangent — what block 21 receives as its dyOut.

⭐ Head, tied — all EIGHT nodes: two conv weights, two BatchNorm γ/β pairs, and the classifier's weight and bias. ⭐ The last two are r34HeadTiedB, reused verbatim: MNv4's GAP-and-dense tail IS ResNet-34's at a different width.

The per-BLOCK forward prefixes: mnv4Blk0 is the fused stage's output — block 1's input — and mnv4Blk{k} is the activation entering block k+1.

⚠ MobileNetV4FullB.lean's mnv4Pre0 … mnv4Pre6 are the RESOLUTION-GROUP prefixes, which is the granularity T1 and T2 need; the tie needs one per BLOCK, so these 22 name the finer chain. mnv4Blk0 is definitionally mnv4Pre1.