Humans and animals excel at generalizing from limited data, a capability yet to be fully
replicated in artificial intelligence. This perspective investigates generalization in biological …

Despite the practical success of deep neural networks, a comprehensive theoretical
framework that can predict practically relevant scores, such as the test accuracy, from …

We analyze feature learning in infinite-width neural networks trained with gradient flow
through a self-consistent dynamical field theory. We construct a collection of deterministic …

We analyze the dynamics of finite width effects in wide but finite feature learning neural
networks. Starting from a dynamical mean field theory description of infinite width deep …

We investigate theoretically how the features of a two-layer neural network adapt to the
structure of the target function through a few large batch gradient descent steps, leading to …

Characterizing how neural network depth, width, and dataset size jointly impact model
quality is a central problem in deep learning theory. We give here a complete solution in the …

We study the effect of width on the dynamics of feature-learning neural networks across a
variety of architectures and datasets. Early in training, wide neural networks trained on …

Feature learning is thought to be one of the fundamental reasons for the success of deep
neural networks. It is rigorously known that in two-layer fully-connected neural networks …

Complex networks pervade various real-world systems, from the natural environment to
human societies. The essence of these networks is in their ability to transition and evolve …

Both the path integral measure in field theory (FT) and ensembles of neural networks (NN)
describe distributions over functions. When the central limit theorem can be applied in the …