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Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Publications associées (37)

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In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

EPFL2024

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Anastasiia Koloskova

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

EPFL2024

The multivariate Serre conjecture ring

Luc Guyot

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

San Diego2023

Linear Complexity Self-Attention With 3rd Order Polynomials

Grigorios Chrysos, Filippos Kokkinos

Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...

Los Alamitos2023

Discriminative clustering with representation learning with any ratio of labeled to unlabeled data

We present a discriminative clustering approach in which the feature representation can be learned from data and moreover leverage labeled data. Representation learning can give a similarity-based clustering method the ability to automatically adapt to an ...

2022

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Ludovic Théo Stephan, Bruno Loureiro

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 net-works, which tend to get stuck in badly-generalizing loca ...

2022

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Volkan Cevher, Ali Kavis

In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...

2021

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Mathieu Hursin

Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the t ...

PERGAMON-ELSEVIER SCIENCE LTD2021

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Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally giv ...

IEEE2020