Neuroscience research is undergoing a minor revolution. Recent advances in machine
learning and artificial intelligence research have opened up new ways of thinking about …

Quantum matter, the research field studying phases of matter whose properties are
intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter …

There is mounting evidence of emergent phenomena in the capabilities of deep learning
methods as we scale up datasets, model sizes, and training times. While there are some …

We identify and formalize a fundamental gradient descent phenomenon resulting in a
learning proclivity in over-parameterized neural networks. Gradient Starvation arises when …

Single-index models are a class of functions given by an unknown univariate``link''function
applied to an unknown one-dimensional projection of the input. These models are …

The practical success of overparameterized neural networks has motivated the recent
scientific study of\emph {interpolating methods}--learning methods which are able fit their …

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in
the high-dimensional regime. We prove limit theorems for the trajectories of summary …

Deep classifier neural networks enter the terminal phase of training (TPT) when training
error reaches zero and tend to exhibit intriguing Neural Collapse (NC) properties. Neural …

Mathematically characterizing the implicit regularization induced by gradient-based
optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is …

Understanding the reasons for the success of deep neural networks trained using stochastic
gradient-based methods is a key open problem for the nascent theory of deep learning. The …