Highlights

Short, informal accounts of some of our papers: the question, the main result, and what it changes.

• How gradient descent finds features in wide networks

  Learning in two-layer networks whose width grows with the input dimension, from a collective, Gaussian stage to the discovery of individual features. Preprint, 2026.

• A theory of feature learning in deep neural networks

  Bayes-optimal learning curves for deep networks whose width and data grow with the input dimension, and the layer-by-layer way in which they learn features. Physical Review X 16, 2026.

• Matrix denoising beyond rotational invariance

  When the factorized structure of a large extensive-rank matrix starts to matter, and a multiscale mean-field theory for the hard phase. Physical Review X 15, 021085, 2025.

• A theory of structured PCA

  What changes in principal component analysis when the noise itself has structure, and an algorithm that reaches the limits. PNAS 120 (30), e2302028120, 2023.