Publications by Emmanuel Abbé

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In 1948, Shannon used a probabilistic argument to show that there exist codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction, conjectured shortly after to achieve chann ...

Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the h ...

Background Quantitative coronary angiography (QCA) permits the objective assessment of coronary artery disease. However, traditional edge detection algorithms often struggle with accurate vessel segmentation due to the complexity and variable quality of angiographic images. As a result, manual correction is frequently needed, which is a major limitation of current QCA systems. Purpose We developed angioPy, a deep learning-driven tool for vessel segmentation that employs user-defined ground truth points to m

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into su ...

Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are still under inv ...

Learning with identical train and test distributions has been extensively investigated both practically and theoretically. Much remains to be understood, however, in statistical learning under distribution shifts. This paper focuses on a distribution shift setting where train and test distributions can be related by classes of (data) transformation maps. We initiate a theoretical study for this framework, investigating learning scenarios where the target class of transformations is either known or unknown.

A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for instance in density estimation or to achieve excess risk bounds derived from single-scale entropy regularizers (Xu-Raginsky '17). This paper investigates a generalization of these results to a multiscale setting. We present different ways of generalizing the maximum entrop

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual principal component scores that yield low-dimensional embedding of samples. That hinders the analysis of various spectral methods. In this paper, we first develop an ℓp perturbation theory for a hollowed version of PCA in Hilbert spaces which provably improv

Spectral algorithms, such as principal component analysis and spectral clustering, rely on the extremal eigenpairs of a matrix A. However, these may be uninformative without preprocessing A with a proper transformation. The reason is that the spectrum of A ...

This paper considers "delta-almost Reed-Muller codes", i.e., linear codes spanned by evaluations of all but a delta fraction of monomials of degree at most d. It is shown that for any delta > 0 and any epsilon > 0, there exists a family of delta-almost Ree ...

Goal: In patients with coronary artery disease, the prediction of future cardiac events such as myocardial infarction (MI) remains a major challenge. In this work, we propose a novel anatomy-informed multimodal deep learning framework to predict future MI ...

Parities have become a standard benchmark for evaluating learning algorithms. Recent works show that regular neural networks trained by gradient descent can efficiently learn degree

k

parities on uniform inputs for constant

k

, but fail to do so when

k

and

d-k

grow with

d

(here

d

is the ambient dimension). However, the case where

k=d-O_d(1)

(almost-full parities), including the degree

d

parity (the full parity), has remained unsettled. This paper shows that for gradient descent on regular neu

Can Transformers predict new syllogisms by composing established ones? More generally, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity, but this does not address the learnability objective. This paper puts forward the notion of globality degree of a target distribution to capture when weak learning is efficiently achievable by regular Transformers. This measure shows a contrast with the expressivity results

The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...

The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for spe ...

Cardiovascular disease is the leading global cause of mortality, with coronary artery disease (CAD) as its most prevalent form, necessitating early risk prediction. While 3D coronary artery digital twins reconstructed from imaging offer detailed anatomy for personalized assessment, their analysis relies on computationally intensive computational fluid dynamics (CFD), limiting scalability. Data-driven approaches are hindered by scarce labeled data and lack of physiological priors. To address this, we present

Non–ST-elevation acute coronary syndrome (NSTE-ACS) remains a diagnostic challenge, as a proportion of patients do not present with obstructive coronary lesions. Coronary computed tomography angiography (CCTA) has emerged as a non-invasive tool for coronary assessment, and integrating artificial intelligence (AI) may enhance its diagnostic accuracy. This study evaluates a machine learning (ML) model using a learned fusion approach to identify culprit lesions in high-risk NSTE-ACS patients. This study is a s

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arıkan’s polarization technique applied individually to each user transforms independent uses of a m-user binary input MAC into suc ...

Emmanuel Abbé

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AN l(p) THEORY OF PCA AND SPECTRAL CLUSTERING

A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels

Chaining Mutual Information and Tightening Generalization Bounds

angioPy: an open-source, deep learning-driven tool for coronary artery segmentation

Polar Codes for the m-User Multiple Access Channel

Reed-Muller Codes

Transformation-invariant Learning and Theoretical Guarantees for Ood Generalization

Maximum Multiscale Entropy and Neural Network Regularization

An $\ell_p$ theory of PCA and spectral clustering

Reed-Muller Codes: Theory and Algorithms

Graph Powering and Spectral Robustness

Almost-Reed-Muller Codes Achieve Constant Rates for Random Errors

Anatomy-Informed Multimodal Learning for Myocardial Infarction Prediction

Learning High-Degree Parities: The Crucial Role of the Initialization

How Far Can Transformers Reason? the Globality Barrier and Inductive Scratchpad

Polynomial-time universality and limitations of deep learning

A New Entropy Power Inequality for Integer-Valued Random Variables

Physics-informed self-supervised learning for predictive modeling of coronary artery digital twins

AI-Driven multi-view learning from CCTA for myocardial infarction diagnosis

Polar Codes for the m-User MAC