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08/27/2023
Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
Recent years witnessed the development of powerful generative models bas...
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05/30/2023
Asymptotic Characterisation of Robust Empirical Risk Minimisation Performance in the Presence of Outliers
We study robust linear regression in high-dimension, when both the dimen...
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05/29/2023
Learning Two-Layer Neural Networks, One (Giant) Step at a Time
We study the training dynamics of shallow neural networks, investigating...
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05/29/2023
Escaping mediocrity: how two-layer networks learn hard single-index models with SGD
This study explores the sample complexity for two-layer neural networks ...
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03/09/2023
Statistical mechanics of the maximum-average submatrix problem
We study the maximum-average submatrix problem, in which given an N × N ...
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03/05/2023
Expectation consistency for calibration of neural networks
Despite their incredible performance, it is well reported that deep neur...
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02/17/2023
Universality laws for Gaussian mixtures in generalized linear models
Let (x_i, y_i)_i=1,…,n denote independent samples from a general mixture...
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02/17/2023
Are Gaussian data all you need? Extents and limits of universality in high-dimensional generalized linear estimation
In this manuscript we consider the problem of generalized linear estimat...
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02/13/2023
Optimal Algorithms for the Inhomogeneous Spiked Wigner Model
In this paper, we study a spiked Wigner problem with an inhomogeneous no...
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02/12/2023
From high-dimensional mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks
This manuscript investigates the one-pass stochastic gradient descent (S...
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02/01/2023
Optimal Learning of Deep Random Networks of Extensive-width
We consider the problem of learning a target function corresponding to a...
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10/23/2022
A study of uncertainty quantification in overparametrized high-dimensional models
Uncertainty quantification is a central challenge in reliable and trustw...
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10/12/2022
Rigorous dynamical mean field theory for stochastic gradient descent methods
We prove closed-form equations for the exact high-dimensional asymptotic...
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08/11/2022
Low-rank Matrix Estimation with Inhomogeneous Noise
We study low-rank matrix estimation for a generic inhomogeneous output c...
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05/26/2022
Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap
A simple model to study subspace clustering is the high-dimensional k-Ga...
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05/26/2022
Multi-layer State Evolution Under Random Convolutional Design
Signal recovery under generative neural network priors has emerged as a ...
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05/26/2022
Gaussian Universality of Linear Classifiers with Random Labels in High-Dimension
While classical in many theoretical settings, the assumption of Gaussian...
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05/18/2022
Secure Coding via Gaussian Random Fields
Inverse probability problems whose generative models are given by strict...
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03/15/2022
Optimal denoising of rotationally invariant rectangular matrices
In this manuscript we consider denoising of large rectangular matrices: ...
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02/07/2022
Theoretical characterization of uncertainty in high-dimensional linear classification
Being able to reliably assess not only the accuracy but also the uncerta...
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02/01/2022
Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks
Despite the non-convex optimization landscape, over-parametrized shallow...
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01/31/2022
Fluctuations, Bias, Variance Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
From the sampling of data to the initialisation of parameters, randomnes...
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01/29/2022
Error Rates for Kernel Classification under Source and Capacity Conditions
In this manuscript, we consider the problem of kernel classification und...
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01/19/2022
Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learning
Unlike the classical linear model, nonlinear generative models have been...
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10/17/2021
Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising
Factorization of matrices where the rank of the two factors diverges lin...
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07/25/2021
LightOn Optical Processing Unit: Scaling-up AI and HPC with a Non von Neumann co-processor
We introduce LightOn's Optical Processing Unit (OPU), the first photonic...
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06/07/2021
Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions
Generalised linear models for multi-class classification problems are on...
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05/31/2021
Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime
In this manuscript we consider Kernel Ridge Regression (KRR) under the G...
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05/16/2021
Bayesian reconstruction of memories stored in neural networks from their connectivity
The advent of comprehensive synaptic wiring diagrams of large neural cir...
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02/23/2021
Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed
A recent series of theoretical works showed that the dynamics of neural ...
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02/16/2021
Capturing the learning curves of generic features maps for realistic data sets with a teacher-student model
Teacher-student models provide a powerful framework in which the typical...
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01/06/2021
Adversarial Robustness by Design through Analog Computing and Synthetic Gradients
We propose a new defense mechanism against adversarial attacks inspired ...
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12/11/2020
Hardware Beyond Backpropagation: a Photonic Co-Processor for Direct Feedback Alignment
The scaling hypothesis motivates the expansion of models past trillions ...
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12/08/2020
Construction of optimal spectral methods in phase retrieval
We consider the phase retrieval problem, in which the observer wishes to...
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09/20/2020
Epidemic mitigation by statistical inference from contact tracing data
Contact-tracing is an essential tool in order to mitigate the impact of ...
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06/25/2020
The Gaussian equivalence of generative models for learning with two-layer neural networks
Understanding the impact of data structure on learning in neural network...
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06/23/2020
Direct Feedback Alignment Scales to Modern Deep Learning Tasks and Architectures
Despite being the workhorse of deep learning, the backpropagation algori...
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06/12/2020
Reservoir Computing meets Recurrent Kernels and Structured Transforms
Reservoir Computing is a class of simple yet efficient Recurrent Neural ...
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06/12/2020
Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval
Despite the widespread use of gradient-based algorithms for optimizing h...
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06/11/2020
Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)
There has been a recent surge of interest in the study of asymptotic rec...
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06/11/2020
Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization
We consider a commonly studied supervised classification of a synthetic ...
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06/10/2020
Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification
We analyze in a closed form the learning dynamics of stochastic gradient...
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06/09/2020
Phase retrieval in high dimensions: Statistical and computational phase transitions
We consider the phase retrieval problem of reconstructing a n-dimensiona...
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06/02/2020
Light-in-the-loop: using a photonics co-processor for scalable training of neural networks
As neural networks grow larger and more complex and data-hungry, trainin...
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04/03/2020
TRAMP: Compositional Inference with TRee Approximate Message Passing
We introduce tramp, standing for TRee Approximate Message Passing, a pyt...
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03/02/2020
Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime
Deep neural networks can achieve remarkable generalization performances ...
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02/26/2020
The role of regularization in classification of high-dimensional noisy Gaussian mixture
We consider a high-dimensional mixture of two Gaussians in the noisy reg...
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02/21/2020
Generalisation error in learning with random features and the hidden manifold model
We study generalised linear regression and classification for a syntheti...
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02/11/2020
Asymptotic errors for convex penalized linear regression beyond Gaussian matrices
We consider the problem of learning a coefficient vector x_0 in R^N from...
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12/05/2019