How does feature learning reshape the function space?
Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the function space spanned by the features of a two-layer neural network evolves during gradient descent training. We prove that, in the high-dimensional proportional regime, after a large gradient step the post-update feature distribution is well approximated by a target-dependent spiked Gaussian covariance. This induces a data-adaptive kernel that reshapes the function space and modifies its spectral structure. Our analysis reveals that feature learning can be...
| Authors | João Lobo, Bruno Loureiro, Long Tran-Than et al. |
|---|---|
| Primary category | stat.ML |
| Published | 18 May 2026 |
| Last updated at source | 18 May 2026 |
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