The Rhythm of Learning: How Kernel Spectra Shape Neural Network Training
![The study demonstrates a decomposition of test error into bias and variance components, revealing that the expectation value of the kernel-following a power law of [latex]\Lambda\_{ij}=i^{-3/2}\delta\_{ij}[/latex]-dictates the trade-off between these error sources, as observed through simulations employing a time step of [latex]\mathrm{d}t=10^{-4}[/latex] and averaged over [latex]10^{5}[/latex] realizations with parameters [latex]\beta=10[/latex] and [latex]g\beta=10^{3}[/latex] at an interpolation threshold of P=N=102, contrasted with theoretical calculations utilizing [latex]\mathrm{d}t=10^{-2}[/latex].](https://arxiv.org/html/2602.23039v1/2602.23039v1/x3.png)
New research reveals the interplay between kernel structure and training dynamics, offering insights into why and how neural networks generalize effectively.
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