arXiv AI June 30, 2026 By Yuto Omae, Kazuki Sakai, Yohei Kakimoto, Makoto Sasaki, Yusuke Sakai, Hirotaka Takahashi

Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks

arXiv:2606. 28662v1 Announce Type: cross Abstract: The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization.

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arXiv Statistics ML

6d ago

A Flatness-Generalization Relation in the Teacher-Student Tree-Committee Machine

arXiv:2609.31101v1 Announce Type: cross Abstract: The flatness of the loss landscape at a minimizer is a widely used heuristic for reasoning about neural-network generalization, yet evidence for this...

By Brandon Livio Annesi, Davide Straziota, Enrico Maria Malatesta

arXiv Machine Learning

Aug 21

R\'enyi Sharpness: A Novel Sharpness that Strongly Correlates with Generalization

arXiv:2510. 07758v3 Announce Type: replace Abstract: Sharpness (of the loss minima) is widely believed to be a good indicator of generalization of neural networks.

By Qiaozhe Zhang, Jun Sun, Ruijie Zhang, Yingzhuang Liu

benchmarks

Hugging Face Trending Papers

Jul 15

How the Hessian-Spectrum of Neural Networks Depends on Data

The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc. Prior works have focused on empirical results or pursued a theoretical treatment under overly simplified settings.

arXiv Machine Learning

Jul 16

How the Hessian-Spectrum of Neural Networks Depends on Data

arXiv:2607. 13631v1 Announce Type: new Abstract: The Hessian matrix is an important quantity of interest when it comes to studying the loss landscape and optimization dynamics in deep learning, as well as designing measures of generalization, second-order learning algorithms, etc.

By Jasraj Singh, Enea Monzio Compagnoni, Antonio Orvieto

arXiv Machine Learning

Jul 16

Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning

arXiv:2605. 07914v2 Announce Type: replace Abstract: Sharpness-aware and gradient-alignment methods have been shown to improve generalization, however each family of methods targets a single geometric property of the loss landscape, while ignoring the other.

By Aristotelis Ballas, Christos Diou

benchmarks safety

arXiv Machine Learning

Aug 11

Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks

arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.

By Po Chen, Rujun Jiang, Peng Wang

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A Flatness-Generalization Relation in the Teacher-Student Tree-Committee Machine

R\'enyi Sharpness: A Novel Sharpness that Strongly Correlates with Generalization

How the Hessian-Spectrum of Neural Networks Depends on Data

How the Hessian-Spectrum of Neural Networks Depends on Data

Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning

Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks