Lenka Zdeborová

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Rigorous Dynamical Mean-Field Theory for Stochastic Gradient Descent Methods

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani

We prove closed-form equations for the exact high-dimensional asymptotics of a family of first-order gradient-based methods, learning an estimator (e.g., M-estimator, shallow neural network) from observations on Gaussian data with empirical risk minimizati ...

Society for Industrial & Applied Mathematics (SIAM)2024

Optimal Inference in Contextual Stochastic Block Models

Lenka Zdeborová

The contextual stochastic block model (CSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine learning on graphs, the ...

2024

Quenches in the Sherrington-Kirkpatrick model

Florent Gérard Krzakala, Lenka Zdeborová, Freya Behrens, Vittorio Erba

The Sherrington-Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that local ...

2024

Backtracking Dynamical Cavity Method

Lenka Zdeborová, Freya Behrens, Barbora Hudcová

The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a broad range of mode ...

American Physical Society2023

Phase diagram of stochastic gradient descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Ludovic Théo Stephan

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local ...

Iop Publishing Ltd2023

Neural-prior stochastic block model

Lenka Zdeborová

The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works modeled such data ...

2023

Multi-layer state evolution under random convolutional design

Florent Gérard Krzakala, Lenka Zdeborová

Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however, challenging. For generati ...

2023

Bayes-optimal inference for spreading processes on random networks

Lenka Zdeborová, Indaco Biazzo

We consider a class of spreading processes on networks, which generalize commonly used epidemic models such as the SIR model or the SIS model with a bounded number of reinfections. We analyze the related problem of inference of the dynamics based on its pa ...

Amer Physical Soc2023

Bayesian reconstruction of memories stored in neural networks from their connectivity

Florent Gérard Krzakala, Lenka Zdeborová

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in ...

2023

High-dimensional Asymptotics of Denoising Autoencoders

Lenka Zdeborová, Hugo Chao Cui

We address the problem of denoising data from a Gaussian mixture using a twolayer non-linear autoencoder with tied weights and a skip connection. We consider the high-dimensional limit where the number of training samples and the input dimension jointly te ...

2023

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