MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration | Signal Canvas | ScienceToStartup

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Proof freshness: stale
Proof status: unverified
Display score: 4/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 70
Source count: 3
Coverage: 50%

This page is showing the last landed evidence receipt and score bundle because the latest proof data is outside the freshness window.

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source_context

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Evidence Receipt

Route status: building

Claims: 8

References: 70

Proof: Verification pending

Freshness state: computing

Source paper: MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

PDF: https://arxiv.org/pdf/2603.28254v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-31T20:22:49.832Z

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Not build-ready: MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

/buildability/muoneq-balancing-before-orthogonalization-with-lightweight-equilibration

Ignoreblocked

Subject: MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

Verdict

Ignore

Verdict is Ignore because current viability and proof state do not clear the buildability gate.

Preparing verified analysis

GitHub Code Pulse

No public code linked for this paper yet.

Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
We introduce {\method}, a lightweight family of pre-orthogonalization equilibration schemes for Muon in three forms: two-sided row/column normalization (RC), row normalization (R), and column normalization (C).
Implicationpartial
Explicitly stated in the abstract and repeated in the analysis section as the core contribution.
Verificationpartial
partial
Evidencepartial
For the hidden matrix weights targeted by {\method}, the row-normalized variant R is the natural default and preserves the $\widetilde{\mathcal{O}}(T^{-1/4})$ stationarity guarantee of Muon-type methods.
Implicationpartial
Directly stated in the abstract as a theoretical property of the proposed method.
Verificationpartial
partial
Evidencepartial
In LLaMA2 pretraining on C4, the default R variant consistently outperforms Muon on 130M and 350M models, yielding faster convergence and lower validation perplexity.
Implicationpartial
Explicitly stated in the abstract and supported by experimental results in Figures 3 and 4.
Verificationpartial
partial
Evidencepartial
Two-sided row/column normalization decays fastest.
Implicationpartial
Strongly supported by the caption and data trend in Figure 2, though the exact claim wording is inferred.
Verificationpartial
partial
Evidencepartial
These variants rebalance the momentum matrix before finite-step Newton--Schulz using row/column squared-norm statistics and only $\mathcal{O}(m+n)$ auxiliary state.
Implicationpartial
Directly stated in the abstract as a key characteristic of the method.
Verificationpartial
partial
Evidencepartial
R performs best on both CIFAR-10/ResNet-18 and FineWeb/GPT2-small, reaching 94.53% test accuracy on CIFAR-10 and 24.94 validation perplexity on FineWeb/GPT2-small.
Implicationpartial
Explicitly stated in the analysis section with specific numeric results.
Verificationpartial
partial
Evidencepartial
We show that finite-step orthogonalization is governed by input spectral properties, especially stable rank and condition number
Implicationpartial
Directly stated in the abstract as a finding from the analysis.
Verificationpartial
partial
Evidencepartial
and that row/column normalization is a zeroth-order whitening surrogate that removes marginal scale mismatch.
Implicationpartial
Directly stated in the abstract as a theoretical interpretation of the method's mechanism.
Verificationpartial
partial

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MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

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