Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

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Proof freshness: stale
Proof status: unverified
Display score: 3/10
Last proof check: 2026-03-30
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 65
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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Evidence Receipt

Route status: building

Claims: 7

References: 65

Proof: Verification pending

Freshness state: computing

Source paper: Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

PDF: https://arxiv.org/pdf/2603.26554v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-30T23:58:31.139Z

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Not build-ready: Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

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Subject: Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

Verdict

Ignore

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

Preparing verified analysis

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Claim map

Strong 7Mixed 0Weak 0

Evidencepartial
Muon storesd 1+ 1/2α items (Theorem 3), whereas GD stores onlyd 1/2α items (Theorem 5).
Implicationpartial
This is a central finding explicitly stated in the abstract and supported by Figure 2a and Theorem 3 vs Theorem 5.
Verificationpartial
partial
Evidencepartial
Muon saturates at a larger critical batch size.
Implicationpartial
Stated in the abstract and supported by Figure 1b and the text discussing critical batch sizes.
Verificationpartial
partial
Evidencepartial
Muon achieves a substantially faster initial recovery rate than SGD
Implicationpartial
This is a key finding from the multi-step analysis, explicitly mentioned in the abstract and supported by Theorem 10.
Verificationpartial
partial
Evidencepartial
the one-step Muon update W1 ∝h λ(G0)recovers all items up to i≲min{n i⋆, B 1/α (logd) − 1/α }
Implicationpartial
This is a specific theoretical result with a precise bound provided in Theorem 3.
Verificationpartial
partial
Evidencepartial
Within this scheme, gradient descent corresponds to h(z) =z, while exact Muon corresponds to h(z) = sign(z).
Implicationpartial
This defines the general framework for spectral optimizers and specifies the forms for GD and Muon.
Verificationpartial
partial
Evidencepartial
Muon storesd 1+ 1/2α items (Theorem 3)
Implicationpartial
This is a precise theoretical result derived in the paper, stated in the abstract and supported by Theorem 3.
Verificationpartial
partial
Evidencepartial
for the first⌈2α⌉steps, the recovery exponent of SGD increases linearly u
Implicationpartial
This is a specific theoretical limitation identified for SGD in multi-step recovery, detailed in Theorem 10.
Verificationpartial
partial

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Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

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