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pith:ON25ECWU

pith:2025:ON25ECWU7YVOFZ7KHJWRFYOHJS

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Feature Learning Dynamics in Infinite-Depth Neural Networks

Ruoyu Wu, Tianxiang Gao, Zihan Yao

Finite ResNet training dynamics converge to a decoupled Neural Feature Dynamics limit with O(L^{-1}) error under depth-μP scaling.

arxiv:2512.21075 v2 · 2025-12-24 · cs.LG · cs.AI · math.PR · stat.ML

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Claims

C1strongest claim

Under nondegeneracy assumptions, we prove that the finite-network training dynamics converge to its NFD limit with an O(L^{-1}) depth-discretization error, while the reused-weight coupling term has a faster O(L^{-2}) decay.

C2weakest assumption

The nondegeneracy assumptions on the feature-gradient covariance structure generated during training, which are required to ensure the SDE limit exists and that the coupling remains higher-order in depth under depth-μP scaling.

C3one line summary

Under depth-μP scaling, the reused-weight forward-backward coupling in one-layer ResNets vanishes at O(L^{-2}), enabling convergence to a decoupled Neural Feature Dynamics SDE limit with O(L^{-1}) discretization error.

References

4 extracted · 4 resolved · 0 Pith anchors

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Cited by

1 paper in Pith

The Effective Depth Paradox: Evaluating the Relationship between Architectural Topology and Trainability in Deep CNNs

Receipt and verification

First computed	2026-05-18T03:09:32.417066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7375d20ad4fe2ae2e7ea3a6d12e1c74c9ce0aeb71e2cad3b977bbf207b8942c1

Aliases

arxiv: 2512.21075 · arxiv_version: 2512.21075v2 · doi: 10.48550/arxiv.2512.21075 · pith_short_12: ON25ECWU7YVO · pith_short_16: ON25ECWU7YVOFZ7K · pith_short_8: ON25ECWU

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/ON25ECWU7YVOFZ7KHJWRFYOHJS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7375d20ad4fe2ae2e7ea3a6d12e1c74c9ce0aeb71e2cad3b977bbf207b8942c1

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "91734d4062d34a7c318692774f524346ae498c97a0a9ae90bc1e897a3636e805",
    "cross_cats_sorted": [
      "cs.AI",
      "math.PR",
      "stat.ML"
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-12-24T09:39:04Z",
    "title_canon_sha256": "f681a678a515c588697b44471af8b50a099a038d207515149b5a0ea0d3534034"
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