4 papers · 1 filter
Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy
Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro
We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent for polynomial inner-product kernels. We…
How does feature learning reshape the function space?
João Lobo, Bruno Loureiro, Long Tran-Than +1
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 under…
Fast Escape, Slow Convergence: Learning Dynamics of Phase Retrieval under Power-Law Data
Guillaume Braun, Bruno Loureiro, Ha Quang Minh +1
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a…
Kernel ridge regression under power-law data: spectrum and generalization
Arie Wortsman, Bruno Loureiro
In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from t…