Pith Number

pith:R73BLH45

pith:2026:R73BLH45A2YJVPTU4VOOZ6R6VB

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Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning

Binghang Lu, Bing Hu, Changhong Mou, Guang Lin, Runyu Zhang, Xiaomin Li, Yuan Tian, Yunhan Zhao, Zheyuan Deng

Spectral-norm geometry with orthogonal projections reduces catastrophic forgetting in sequential LLM fine-tuning.

arxiv:2605.08949 v2 · 2026-05-09 · cs.LG

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Claims

C1strongest claim

Muon-OGD consistently improves over sequential fine-tuning and competitive orthogonal-gradient baselines by applying spectral-norm-aware update geometry with orthogonalized momentum updates that avoid protected directions associated with prior tasks.

C2weakest assumption

That spectral-norm geometry is more suitable than Frobenius norm for matrix-valued LLM parameters, as suggested by the empirical success of the Muon optimizer, and that the resulting constrained optimization can be solved efficiently without compromising the non-interference guarantees.

C3one line summary

Muon-OGD introduces a spectral-norm constrained orthogonal projection method solved via dual iterations and Newton-Schulz approximations to improve stability-plasticity trade-off in sequential LLM adaptation.

References

48 extracted · 48 resolved · 8 Pith anchors

[1] Overcoming catastrophic forgetting in neural networks.Proceedings of the national academy of sciences, 114(13):3521–3526 2017

[2] An empirical investigation of catastrophic forgetting in gradient-based neural networks.arXiv preprint arXiv:1312.6211 2013 · arXiv:1312.6211

[3] Continual learning with deep generative replay.Advances in neural information processing systems, 30 2017

[4] Lifelong learning with dynamically expandable networks 2018

[5] Learning without forgetting.IEEE transactions on pattern analysis and machine intelligence, 40(12):2935–2947 2017

Formal links

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Cited by

1 paper in Pith

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Receipt and verification

First computed	2026-05-20T00:00:41.771762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ff6159f9d06b09abe74e55cecfa3ea8500f9575464183abd463ef92835a343a

Aliases

arxiv: 2605.08949 · arxiv_version: 2605.08949v2 · doi: 10.48550/arxiv.2605.08949 · pith_short_12: R73BLH45A2YJ · pith_short_16: R73BLH45A2YJVPTU · pith_short_8: R73BLH45

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R73BLH45A2YJVPTU4VOOZ6R6VB \
  | 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: 8ff6159f9d06b09abe74e55cecfa3ea8500f9575464183abd463ef92835a343a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e41baa924b7c84a8c651311634366eb397c03503c36920ec0ac0e42a78e490f7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-09T13:42:08Z",
    "title_canon_sha256": "3f0a057ff859e968774069b12909d97b2786e1f57687776717abc66d0785e963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08949",
    "kind": "arxiv",
    "version": 2
  }
}