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abstract indexed · arXiv 2609.17759 · updated 2026-10-18

Derivative-Free Structured Updates for Muon

First page of Derivative-Free Structured Updates for Muon
From the original paper · arXiv 2609.17759Page 1. Select the image to read the PDF.

The method replaces gradient-based momentum in the Muon optimizer with structured finite-difference probes (entrywise, random low-rank, basis-aligned rank-one, or direct search) orthogonalized into Muon-style updates. The cost is a large number of additional function evaluations per update step, plus reduced update accuracy when probing is subsampled, and it carries no convergence guarantee. It fails to help whenever reliable, inexpensive backpropagation gradients are available, which covers essentially all standard model training on a single-GPU budget.

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What to measure

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research area
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Derivative-free Muon updates via structured finite-difference probing
published
2026-09-15

The paper addresses black-box problems with unavailable or unreliable gradients, a niche the reader with constrained infrastructure rarely faces in production training, and the paper itself disclaims any advantage over accurate, inexpensive gradients.

About the technical core

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  1. claim 01Paperraft inference
    Read the brief interpretation

    The method replaces gradient-based momentum in the Muon optimizer with structured finite-difference probes (entrywise, random low-rank, basis-aligned rank-one, or direct search) orthogonalized into Muon-style updates. The cost is a large number of additional function evaluations per update step, plus reduced update accuracy when probing is subsampled, and it carries no convergence guarantee. It fails to help whenever reliable, inexpensive backpropagation gradients are available, which covers essentially all standard model training on a single-GPU budget.

    This is a Paperraft inference. It is not pinned to a verified PDF passage.

    Inspect the source
  2. claim 02Paperraft inference

    Random rank-one probing reduces the number of function evaluations substantially relative to exhaustive probing, at the cost of less accurate updates; no quantitative factor or advantage over accurate inexpensive gradients is reported.

    This is a Paperraft inference. It is not pinned to a verified PDF passage.

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quality

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compute and memory

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latency

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operations

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software compatibility

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security

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data and training

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reproducibility

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Inside the paper

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Provisional research brief updated 2026-10-18. Paperraft has not reproduced this experiment.

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arXiv 2609.17759

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