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Deep learning Hessian spectra explained by hidden symmetry

A new paper published on arXiv explores the spectral properties of the Hessian matrix in deep learning models. Researchers have observed that eigenvalues in trained models tend to cluster, with a large group near zero and a few outliers. This study proposes that these patterns arise from a hidden, highly symmetric reference configuration. Modifications to the model architecture, data, or parameter metric break this symmetry, leading to the observed eigenvalue distribution. AI

IMPACT Provides a theoretical framework for understanding model behavior and potential avenues for architectural improvements.

RANK_REASON The cluster contains a research paper published on arXiv detailing theoretical findings about deep learning. [lever_c_demoted from research: ic=1 ai=1.0]

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Deep learning Hessian spectra explained by hidden symmetry

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The cluster contains a research paper published on arXiv detailing theoretical findings about deep learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yossi Arjevani ·

    Eigenvalues of the Hessian in Deep Learning: The Origin of Symmetry and Its Breaking

    arXiv:2610.09919v1 Announce Type: new Abstract: Hessian spectra at trained models in deep learning exhibit a persistent pattern: eigenvalues organize into distinct clusters, including a large bulk near zero and a few isolated outliers. This paper shows that a natural account of t…