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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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06/05/2023
Gibbs Sampling the Posterior of Neural Networks
In this paper, we study sampling from a posterior derived from a neural ...
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05/18/2023
High-dimensional Asymptotics of Denoising Autoencoders
We address the problem of denoising data from a Gaussian mixture using a...
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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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02/01/2023
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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10/15/2022
Disordered Systems Insights on Computational Hardness
In this review article, we discuss connections between the physics of di...
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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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09/07/2022
Planted matching problems on random hypergraphs
We consider the problem of inferring a matching hidden in a weighted ran...
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08/12/2022
The planted XY model: thermodynamics and inference
In this paper we study a fully connected planted spin glass named the pl...
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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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03/22/2022
Learning curves for the multi-class teacher-student perceptron
One of the most classical results in high-dimensional learning theory pr...
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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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02/21/2022
(Dis)assortative Partitions on Random Regular Graphs
We study the problem of assortative and disassortative partitions on ran...
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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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01/29/2022
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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12/24/2021
Aligning random graphs with a sub-tree similarity message-passing algorithm
The problem of aligning Erdös-Rényi random graphs is a noisy, average-ca...
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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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06/09/2021
Probing transfer learning with a model of synthetic correlated datasets
Transfer learning can significantly improve the sample efficiency of neu...
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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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03/08/2021
Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem
In this paper we investigate how gradient-based algorithms such as gradi...
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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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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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12/01/2020
Solvable Model for Inheriting the Regularization through Knowledge Distillation
In recent years the empirical success of transfer learning with neural n...
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10/26/2020
The planted k-factor problem
We consider the problem of recovering an unknown k-factor, hidden in a w...
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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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06/27/2020
Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions
We study the dynamics of optimization and the generalization properties ...
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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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06/12/2020
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
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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05/22/2020
Recovery thresholds in the sparse planted matching problem
We consider the statistical inference problem of recovering an unknown p...
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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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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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01/02/2020
Thresholds of descending algorithms in inference problems
We review recent works on analyzing the dynamics of gradient-based algor...
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12/09/2019
Large deviations for the perceptron model and consequences for active learning
Active learning is a branch of machine learning that deals with problems...
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12/05/2019
Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning
Statistical learning theory provides bounds of the generalization gap, u...
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12/04/2019
Exact asymptotics for phase retrieval and compressed sensing with random generative priors
We consider the problem of compressed sensing and of (real-valued) phase...
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09/25/2019