Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

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 …

Recent years witnessed the development of powerful generative models based on flows,
diffusion, or autoregressive neural networks, achieving remarkable success in generating …

In this paper, we propose a general framework for tensor singular value decomposition
(tensor singular value decomposition (SVD)), which focuses on the methodology and theory …

These notes survey and explore an emerging method, which we call the low-degree
method, for understanding statistical-versus-computational tradeoffs in high-dimensional …

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

We consider the problem of learning a target function corresponding to a singlehidden layer
neural network, with a quadratic activation function after the first layer, and random weights …

Inference problems with conjectured statistical-computational gaps are ubiquitous
throughout modern statistics, computer science, statistical physics and discrete probability …

In recent years important progress has been achieved towards proving the validity of the
replica predictions for the (asymptotic) mutual information (or “free energy”) in Bayesian …