The bias-variance trade-off is a central concept in supervised learning. In classical statistics,
increasing the complexity of a model (eg, number of parameters) reduces bias but also …

Current deep neural networks are highly overparameterized (up to billions of connection
weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient …

The success of deep learning has revealed the application potential of neural networks
across the sciences and opened up fundamental theoretical problems. In particular, the fact …

In classical statistics, the bias-variance trade-off describes how varying a model's complexity
(eg, number of fit parameters) affects its ability to make accurate predictions. According to …

We study the binary and continuous negative-margin perceptrons as simple nonconvex
neural network models learning random rules and associations. We analyze the geometry of …

We characterise the learning of a mixture of two clouds of data points with generic centroids
via empirical risk minimisation in the high dimensional regime, under the assumptions of …

In these pedagogic notes I review the statistical mechanics approach to neural networks,
focusing on the paradigmatic example of the perceptron architecture with binary an …

Recent works demonstrated the existence of a double-descent phenomenon for the
generalization error of neural networks, where highly overparameterized models escape …

Linear separability, a core concept in supervised machine learning, refers to whether the
labels of a data set can be captured by the simplest possible machine: a linear classifier. In …

Empirical studies on the landscape of neural networks have shown that low-energy
configurations are often found in complex connected structures, where zero-energy paths …