arXiv Open Access 2024

Stochastic weight matrix dynamics during learning and Dyson Brownian motion

Gert Aarts Biagio Lucini Chanju Park

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Abstrak

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.

Topik & Kata Kunci

cond-mat.dis-nn cs.LG hep-lat

Penulis (3)

Gert Aarts

Biagio Lucini

Chanju Park

Format Sitasi

APA MLA BibTeX

Aarts, G., Lucini, B., Park, C. (2024). Stochastic weight matrix dynamics during learning and Dyson Brownian motion. https://arxiv.org/abs/2407.16427

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓