Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for ...
| Authors | Yatin Dandi, Matteo Vilucchio, Luca Arnaboldi et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 May 2026 |
| Last updated at source | 4 September 2026 |
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