The recent striking success of deep neural networks in machine learning raises profound
questions about the theoretical principles underlying their success. For example, what can …

Several recent trends in machine learning theory and practice, from the design of state-of-
the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under …

Graph theory is now becoming a standard tool in system-level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network structure does not …

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 …

Many qualitative features of the emerging collective dynamics in neuronal networks, such as
correlated activity, stability, response to inputs, and chaotic and regular behavior, can be …

Understanding the behaviors of ecological systems is challenging given their multifaceted
complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random …

Stochastic gradient descent (SGD) is the workhorse algorithm of deep learning technology.
At each step of the training phase, a mini batch of samples is drawn from the training dataset …

Cortical networks that have been found to operate close to a critical point exhibit joint
activations of large numbers of neurons. However, in motor cortex of the awake macaque …

This article is part of the Physical Review Research collection titled Physics of
Neuroscience. Recurrent networks are widely used as models of biological neural circuits …