Author

Li Ziyin

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Preprint Aug 2026

Width-Independent Compressibility of Deep Neural Networks

A uniform compressibility theorem for deep multilayer perceptrons with analytic activations is proved, which involves a novel derivative-matching technique which is aware of the low-dimensional input, and a layer-wise reweighting that preserves the input-output mapping.

Hong-Yi Wang, Mingze Wang, Li Ziyin · 0 citations

Preprint Aug 2026

Neural Quadratic Forms: A Unified Minimal Model for Sudden Learning and Scaling Laws

It is shown that a symmetry fixes what variables are: a network layer is a sum over interchangeable units, so relabeling the units leaves it unchanged; given smoothness and the condition that a unit's gradient vanish at the origin, symmetry then enforces a universal leading form for the expansion about the near-zero we...

Zi-Yin Liu, Yi-Zhou Xu, Tomaso A. Poggio et al. · 0 citations