math.OC · 2026-08-06 · No. 76

Optimization and Control, 2026-08-06.

2 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations

    Thang Do, Steffen Dereich, Arnulf Jentzen

    math.OC · cs.LG

    Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs). In many relevant artificial intelligence (AI) systems - such as popular large language models (LLMs)-not the standard SGD scheme is used as the optimization method but instead suitable accelerated variants of SGD are employed. One of the most popular methods of such accelerated SGD variants is the momentum...

    arxiv.org/abs/2608.04607 · PDF

  2. 02

    A Counterexample to Fourier Alignment in Single-Neuron Modular Addition

    Gautam Neelakantan Memana

    math.OC · cs.LG · cs.NE

    We give a negative solution to MAIS-O60. We first construct an example in which an initially active ReLU neuron becomes completely inactive in finite time and thereafter remains frozen at a limit whose Fourier energy is equally distributed among all nonzero real frequency classes. The counterexample holds on an open set of initial conditions and therefore occurs with positive probability under Gaussian initialization. An appendix prepared by...

    arxiv.org/abs/2608.04451 · PDF

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