Why Shallow Neural Networks Learn Sinusoidal Components First: An Orthogonal Polynomial Dynamics Framework

arXiv:2610.21964v1 Announce Type: cross Abstract: Neural networks often learn low-frequency components before high-frequency ones --- a phenomenon called spectral bias or termed F-principle. Many numerical studies have demonstrated this phenomenon, and theoretical studies have sought to explain it. However, several goals remain insufficiently addressed: (1) explaining spectral bias asymptotically, including its origin and why the preferred components are generally sinusoidal; (2) extending the explanation to general activation functions, such as sigmoid and ReLU; (3) making weak assumptions ab

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