Pith Number

pith:Q7RP75NJ

pith:2026:Q7RP75NJCFUMSVMKU25HEF2AWR

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Rethinking Neural Network Learning Rates: A Stackelberg Perspective

Sihan Zeng, Sujay Bhatt, Sumitra Ganesh

Assigning a smaller learning rate to body layers and a larger learning rate to the final layer is equivalent to two-time-scale alternating gradient descent on a Stackelberg reformulation of neural network training.

arxiv:2605.15530 v1 · 2026-05-15 · cs.LG

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Claims

C1strongest claim

training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpreted as a two-time-scale alternating gradient descent algorithm applied to a Stackelberg reformulation of the original objective. We establish finite-time convergence guarantees for the algorithm under broad conditions that accommodate constraint sets and non-smooth activation functions.

C2weakest assumption

The training dynamics of a neural network can be accurately captured by a Stackelberg game in which the final layer is the leader whose objective is defined on the followers' best response; this reformulation must preserve the original optimization landscape sufficiently for the convergence and curvature claims to transfer back to standard training.

C3one line summary

Non-uniform learning rates correspond to a Stackelberg reformulation of the training objective whose two-time-scale alternating gradient descent yields finite-time convergence and can accelerate training through stronger optimization structure and sharper early curvature.

References

16 extracted · 16 resolved · 2 Pith anchors

[1] Ultra-fast fea- ture learning for the training of two-layer neural net- works in the two-timescale regime.arXiv preprint arXiv:2504.18208,

[2] Closed-Form Last Layer Optimization · arXiv:2510.04606

[3] Stochastic gradient methods with layer- wise adaptive moments for training of deep networks 1905

[4] Noise- adaptive layerwise learning rates: Accelerating geometry- aware optimization for deep neural network training

[5] Large batch training does not need warmup.arXiv preprint arXiv:2002.01576, 2002

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:03.658498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87e2fff5a91168c9558aa6ba721740b448e77fceb44c662c8f4e5e1d16959941

Aliases

arxiv: 2605.15530 · arxiv_version: 2605.15530v1 · doi: 10.48550/arxiv.2605.15530 · pith_short_12: Q7RP75NJCFUM · pith_short_16: Q7RP75NJCFUMSVMK · pith_short_8: Q7RP75NJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q7RP75NJCFUMSVMKU25HEF2AWR \
  | 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: 87e2fff5a91168c9558aa6ba721740b448e77fceb44c662c8f4e5e1d16959941

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6a1f834261719ca90efaa28d358065ad5649c7b5fc8d826fbc25614199b3e5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-15T01:59:10Z",
    "title_canon_sha256": "3030629c6c60df30f956abb675863bd5b4868cf177fb8c0f69193342135f5fc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15530",
    "kind": "arxiv",
    "version": 1
  }
}