A "feature ODE" describing the learning behavior of shallow MLPs on simple functions
We study the gradient flow training dynamics of two-layer multi-layer perceptrons (MLPs) on anisotropic Gaussian data. Even in this simple setting, solving the dynamics in full is notoriously difficult, so we try something different. We propose a "feature ODE" that might be intuitively expected to describe the learning dynamics of a shallow MLP. We find that MLPs trained to learn simple target functions (low-order Hermite polynomials and staircase functions) actually roughly follow the loss trajectories from this feature ODE. This agreement is a surprise because of the size of the simplification and the fact that it does not come from a rigorous chain of approximations. We discuss this su...
| Authors | Joseph Turnbull, Berkan Ottlik, Jamie Simon |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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