Empirical evidence shows that fully-connected neural networks in the infinite-width limit (lazy
training) eventually outperform their finite-width counterparts in most computer vision tasks; …

Feature-learning deep nets progressively collapse data to a regular low-dimensional
geometry. How this phenomenon emerges from collective action of nonlinearity, noise …

Previous influential work showed that infinite width limits of neural networks in the lazy
training regime are described by kernel machines. Here, we show that neural networks …

We theoretically characterize gradient descent dynamics in deep linear networks trained at
large width from random initialization and on large quantities of random data. Our theory …

Deep linear networks have been extensively studied, as they provide simplified models of
deep learning. However, little is known in the case of finite-width architectures with multiple …

We study the distributional properties of linear neural networks with random parameters in
the context of large networks, where the number of layers diverges in proportion to the …

Perturbation theory is universally recognized as a fundamental tool in modern theoretical
physics. In the functional integral formalism, perturbation theory provides a method for …

The Bayesian approach has proven to be a valuable tool for analytical inspection of neural
networks. Recent theoretical advances have led to the development of an effective statistical …