15 accepted papers
Classifier-Free Guidance (CFG) is widely used in diffusion and flow-based generative models for high-quality conditional generation, yet its theoretical properties remain incompletely understood. By connecting CFG to the high-dimensional framework of diffusion regimes, we show that in sufficiently h…
In this paper, we leverage existing statistical methods to better understand feature learning from data. We tackle this by modifying the model-free variable selection method, Feature Ordering by Conditional Independence (FOCI), which is introduced in Azadkia & Chatterjee (2021). While FOCI is based…
Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from…
In this paper, we investigate the feature encoding process in a prototypical energy-based generative model, the Restricted Boltzmann Machine (RBM). We start with an analytical investigation using simplified architectures and data structures, and end with numerical analysis of real trainings on real…
We study the training dynamics of a shallow neural network with quadratic activation functions and quadratic cost in a teacher-student setup. In line with previous works on the same neural architecture, the optimization is performed following the gradient flow on the population risk, where the avera…
Pruning methods can considerably reduce the size of artificial neural networks without harming their performance and in some cases they can even uncover sub-networks that, when trained in isolation, match or surpass the test accuracy of their dense counterparts. Here, we characterize the inductive b…
Convolutional architectures have proven extremely successful for vision tasks. Their hard inductive biases enable sample-efficient learning, but come at the cost of a potentially lower performance ceiling. Vision Transformers (ViTs) rely on more flexible self-attention layers, and have recently outp…
One of the central features of modern machine learning models, including deep neural networks, is their generalization ability on structured data in the over-parametrized regime. In this work, we consider an analytically solvable setup to investigate how properties of data impact learning in classi…
Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a singl…
Despite the widespread use of gradient-based algorithms for optimising high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we focus on gradient flow dynamics for phase retr…
Deep neural networks can achieve remarkable generalization performances while interpolating the training data. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent"—a mark of the beneficial role of overparametrization. In this work, we d…
A recent line of research has highlighted the existence of a ``double descent'' phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks to peak when N is of the same order as the number of parameters P. In earlier works, a…
Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than Fully-Connected Networks (FCNs) on spatially structured data…
Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones.H…
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are the complexity of the loss-landscape and of the dynamics within it, and to what extent DNNs share similarities with glass…