A Function-Space Approach to the Statistical Mechanics of Learning Dynamics
In the kernel regime, neural-network learning inherits its preferences from a frozen spectrum. During feature learning, this spectrum evolves, yet networks retain systematic biases toward simple, smooth directions. We develop a function-space statistical framework explaining the origin of these preferences, treating functions and their learning operators as macroscopic variables, with parameterization entering through the multiplicity of parameter configurations realizing each function. For mean-squared loss, error relaxes exactly under the evolving learning operator $M=JJ^\ast$. Training stochasticity induces a Gaussian weight over function-space states, while parameter multiplicity cont...
| Authors | Yizhou Zhang, Weichen Wu, Lun Du et al. |
|---|---|
| Primary category | cs.AI |
| Published | 9 September 2026 |
| Last updated at source | 5 October 2026 |
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