Author

Florent Krzakala

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#machine learning May 2026

Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

Neural Low-Degree Filtering (Neural LoFi) is introduced, a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure and provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime.

Yatin Dandi, Matteo Vilucchio, Luca Arnaboldi et al. · arXiv.org · 1 citation

#machine learning Preprint Sep 2026

High-Dimensional Learning Dynamics of Attention-Indexed Models

This work studies attention-indexed models, a broad framework that can represent multi-layer and multi-head attention architectures, and reveals that attention parameterization itself can act as an architectural implicit bias.

Yi-Zhou Xu, M. Sagitova, L. Zdeborová et al. · 0 citations

Preprint Aug 2026

Spectral phase transitions in Gaussian multi-index models

It is proved that the AMP-derived preprocessing of [Defilippis et al., 2025] is optimal among all bounded matrix-valued preprocessing maps of any fixed dimension and the general spectral conjecture of [Defilippis et al., 2025] is proved.

Florent Krzakala, Pierre Mergny, Vanessa Piccolo · 0 citations