6 papers
A theory of learning data statistics in diffusion models, from easy to hard
Lorenzo Bardone, Claudia Merger, Sebastian Goldt
While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing t…
A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization
Vicente Conde Mendes, Lorenzo Bardone, Cédric Koller +4
Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data i…
Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions
Fabiola Ricci, Lorenzo Bardone, Sebastian Goldt
Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the obse…
Sliding down the stairs: how correlated latent variables accelerate learning with neural networks
Lorenzo Bardone, Sebastian Goldt
Neural networks extract features from data using stochastic gradient descent (SGD). In particular, higher-order input cumulants (HOCs) are crucial for their performance. However, e…
Learning from higher-order statistics, efficiently: hypothesis tests, random features, and neural networks
Eszter Székely, Lorenzo Bardone, Federica Gerace +1
Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between t…
A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
Riccardo Rende, Luciano Loris Viteritti, Lorenzo Bardone +2
Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are chal…