MobileNetV4-Conv-M with stochastic depth and classifier dropout — forward, graph, faithfulness #
MobileNetV4FullB states the net and its classifier-dropout form (mnv4FwdGraphBFullDo). The
paper-tier train steps mnv4in_acc{,dp}8x128wxdropdowd01bf16 also carry stochastic depth
(sd, the %dp<k> inputs): a per-example scale dropPath on the residual BRANCH, after the
project BN and before the skip add, at each of the eighteen skip rows. Site k is the k-th
skip row in table order (the renderer's mnv4DropSites):
| site | 0 | 1–7 | 8–17 |
|---|---|---|---|
| rows | 2 | 4–10 | 12–21 |
The three strided rows (1, 3, 11) have no skip and no site. This file states that forward with
both regularisers, as the renderer's uibFwdSkipB … (drop := some k) and mnv4HeadFwdB … (cd := true) emit them, and proves the typed graph denotes it:
mnv4FwdGraphBFullDrop_faithful— the graph denotesmobilenetv4ForwardBFullDrop, at every pair of masks;mobilenetv4ForwardBFullDrop_sdOnes— at the all-ones drop masks the forward is the dropout forwardmobilenetv4ForwardBFullDo;mobilenetv4ForwardBFullDrop_ones— at all-ones masks everywhere it ismobilenetv4ForwardBFull, exactly (the keep probability is folded into the mask,Training/DropPath).
Those two artifacts are bf16; this is their f32 form, as mnv4FwdGraphBFullDo is for the
classifier-dropout ones. The train steps' backward through the drop sites is outside this
statement, as it is outside MobileNetV4StepTieB.
Why a separate file, and why rw. MobileNetV4FullB's group graphs are private and their
whole-net proof is the one whose simp only spelling dies in the kernel, so the drop-carrying
groups are new definitions here rather than edits there. Every group and whole-net step below is
an outside-in rw with a faithfulness lemma of the shape den <subgraph> = <sub>.fwd (den ·),
so den never meets a literal-width term it could start evaluating.
References #
- Huang et al. 2016, Deep Networks with Stochastic Depth. https://arxiv.org/abs/1603.09382
- Qin et al. 2024, MobileNetV4: Universal Models for the Mobile Ecosystem. https://arxiv.org/abs/2404.10518
A skip row with its stochastic-depth site: the body's output scaled per example by s,
then the identity skip — the reference's x + _drop_branch(body(x)).
Equations
- Proofs.StableHLO.mnv4SkipDrop f s = Proofs.residual (Proofs.dropPath N n s ∘ f)
Instances For
A skip row's graph with its drop site: mnv4SkipGraphB with a dropPathB on the body's
output, mask input mN (the renderer's is dpName k). Like mnv4SkipGraphB, a named
combinator so the block input occurs once in the whole-net term.
Equations
- Proofs.StableHLO.mnv4SkipDropGraphB mN s body e = (Proofs.StableHLO.SHlo.dropPathB mN s (body e)).addVB e
Instances For
A drop-carrying skip row denotes mnv4SkipDrop of whatever its body denotes — generic in
both, so one theorem covers all eighteen.
Trunk group Res28 with its drop site: row 2 reads site 0.
Equations
- One or more equations did not get rendered due to their size.
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Trunk group Res14a with its drop sites: rows 4–6 read sites 1–3.
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Trunk group Res14b with its drop sites: rows 7–10 read sites 4–7.
Equations
- One or more equations did not get rendered due to their size.
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Trunk group Res7a with its drop sites: rows 12–15 read sites 8–11.
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- One or more equations did not get rendered due to their size.
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Trunk group Res7b with its drop sites: rows 16–21 read sites 12–17.
Equations
- One or more equations did not get rendered due to their size.
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At the all-ones masks each group is its CertLayer's forward. Stated against the
*_fwd_apply expansions, where the terms are variables.
MobileNetV4-Conv-M with stochastic depth and classifier dropout:
mobilenetv4ForwardBFullDo with sd's eighteen per-example scales on the skip rows'
branches (site k = the k-th skip row, the module's table) and m before the classifier.
Equations
- One or more equations did not get rendered due to their size.
Instances For
At the all-ones drop masks the forward is the classifier-dropout forward.
At the all-ones masks the forward is mobilenetv4ForwardBFull, exactly.
The MobileNetV4-Conv-M forward graph with stochastic depth and classifier dropout — the
f32 typed form of the forward half of mnv4in_acc{,dp}8x128wxdropdowd01bf16: each skip row's
drop site reads %dp<k> at its site index k, the classifier dropout the input mName (the
render's is doName).
Equations
- One or more equations did not get rendered due to their size.
Instances For
The graph denotes the forward, at every pair of masks — eight outside-in rewrites, as
mnv4FwdGraphBFullDo_faithful.