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Muon updates matrix-valued neural-network parameters by orthogonalizing a gradient-based momentum matrix. Its reliance on derivatives limits its use when gradients are unavailable or unreliable. We develop a derivative-free framework that constructs Muon-style updates from structured finite differences. Four variants a...
It is shown that the contradiction in experience with neural surrogates in derivative-free optimisation dissolves once three factors are stated, and that these, rather than the fit accuracy a training curve reports, are what delimit when a learned local model pays.
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