arXiv Machine Learning
5d ago

Stable initialization without the CLT

The paper introduces a new method called uniform‑phase initialization for deep neural networks with sine activations, eliminating the need for the Central Limit Theorem and fully decoupling layers. This approach avoids distributional approximation errors and coupling between layers, leading to stable weight initialization. Experiments show that models using this initialization outperform state‑of‑the‑art methods on image and audio fitting tasks and remain competitive without tuning, while also supporting μP width scaling.

By Simon Kuang, Kyle Chickering, Xinfan Lin
arXiv Machine Learning
Sep 11

Learning Orthogonal Multi-Index Models Beyond Small Initialization: Incremental Learning, Competitive Dynamics and Symmetry

The paper investigates how two‑layer polynomial‑width neural networks learn orthogonal multi‑index targets under standard initialization. It shows that incremental learning still occurs: the loss decreases sequentially following the Hermite expansion, with lower‑order components learned first. The dynamics also exhibit a competitive reallocation of parameter mass, shifting into the target subspace and concentrating on aligned neurons. The analysis uses a symmetry‑based finite‑width approximation and demonstrates that vanilla gradient descent displays the same qualitative behavior.

By Mo Zhou, Weihang Xu, Simon S. Du, Maryam Fazel
arXiv Machine Learning
Jun 30

Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations

arXiv:2606. 23129v2 Announce Type: replace-cross Abstract: Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias.

By Alex Costanzino, Pierluigi Zama Ramirez, Giuseppe Lisanti, Luigi Di Stefano