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Stochastic weight matrix dynamics during learning and Dyson Brownian motion

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arxiv 2407.16427 v2 pith:NQR7YMOW submitted 2024-07-23 cond-mat.dis-nn cs.LGhep-lat

classification cond-mat.dis-nncs.LGhep-lat
keywords learningbrowniandysonfeaturesmatrixmotionweightwigner
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We demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity to the ratio of the learning rate and the mini-batch size, providing more robust evidence to a previously conjectured scaling relationship. We discuss universal and non-universal features in the resulting Coulomb gas distribution and identify the Wigner surmise and Wigner semicircle explicitly in a teacher-student model and in the (near-)solvable case of the Gaussian restricted Boltzmann machine.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stochastic Quantization as Optimal Control

    hep-lat 2026-07 conditional novelty 6.0 of 10

    Stochastic quantization is re-expressed as finite-time optimal control, in which a learned Doob force plus exact path weights reach the Gibbs measure without waiting for equilibrium.

  2. Random Matrix Theory for Stochastic Gradient Descent

    hep-lat 2024-12 conditional novelty 4.0 of 10

    SGD weight-matrix eigenvalue fluctuations follow random matrix predictions, with variance proportional to learning rate divided by batch size, the linear scaling rule.

  3. Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics

    hep-lat 2025-01 unverdicted novelty 1.0 of 10

    A perspective article reviewing physics-driven machine learning for inverse problems in QCD, without introducing new data, derivations, or quantitative results.

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