Person

Emmanuel Abbé

Related publications (43)

Anatomy-informed multimodal learning for myocardial infarction prediction

Pascal Frossard, Emmanuel Abbé, Stéphane Fournier, Ntorina Thanou, Ivan-Daniel Sievering, Ortal Yona Senouf, Thabodhan Mahendiran, Olivier Muller

2022

Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels

Emmanuel Abbé

We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

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

Emmanuel Abbé, Jan Hazla, Ido Nachum

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 ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Reed-Muller Codes: Theory and Algorithms

Emmanuel Abbé, Min Ye

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 ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Predicting future myocardial infarction from angiographies with deep learning

Pascal Frossard, Emmanuel Abbé, Stéphane Fournier, Ntorina Thanou, David Meier, Nicolas Dayer, Farhang Aminfar, Omar Raita, Ortal Yona Senouf, Thabodhan Mahendiran, Olivier Muller

In patients with stable Coronary Artery Disease (CAD), the identification of lesions which will be responsible of a myocardial infarction (MI) during follow-up remains a daily challenge. In this work, we propose to predict culprit stenosis by applying a de ...

2021

Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Networks

Emmanuel Abbé

We derive generalization and excess risk bounds for neural networks using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural networks and b ...

Microtome Publishing2020

Graph Powering and Spectral Robustness

Emmanuel Abbé

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 ...

SIAM PUBLICATIONS2020

Polarization in Attraction-Repulsion Models

Emmanuel Abbé

This paper introduces a model for opinion dynamics, where at each time step, randomly selected agents see their opinions - modeled as scalars in [0, 1] - evolve depending on a local interaction function. In the classical Bounded Confidence Model, agents op ...

IEEE2020

System and method for decoding reed-muller codes

Emmanuel Abbé, Min Ye

Various embodiments are directed to Reed-Muller decoding systems and methods based on recursive projections and aggregations of cosets decoding, exploiting the self-similarity of RM codes, and extended with list-decoding procedures and with outer-code conc ...

2020

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Emmanuel Abbé, Min Ye

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM code ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Reed-Muller Codes Polarize

Emmanuel Abbé

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are gen ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Reed-Muller codes polarize

Emmanuel Abbé, Min Ye

IEEE COMPUTER SOC2019

Entropic Matroids and Their Representation

Emmanuel Abbé

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw ...

2019

Subadditivity Beyond Trees and the Chi-Squared Mutual Information

Emmanuel Abbé, Enric Boix Adsera

Evans et al. [1] proved the subadditivity of the mutual information in the broadcasting on tree model with binary vertex labels and symmetric edge channels. They raised the question of whether such subadditivity extends to loopy graphs in some appropriate ...

IEEE2019

Chaining Mutual Information and Tightening Generalization Bounds

Emmanuel Abbé

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 ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Polarization of the Renyi Information Dimension With Applications to Compressed Sensing

Emmanuel Abbé, Saeid Haghighatshoar

In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi Information Dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the R ...

Ieee-Inst Electrical Electronics Engineers Inc2017

A New Entropy Power Inequality for Integer-Valued Random Variables

Emmanuel Abbé, Saeid Haghighatshoar

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 ...

Institute of Electrical and Electronics Engineers2014

Polar Codes For Broadcast Channels

Emmanuel Abbé, Michael Christoph Gastpar, Naveen Goela

Building on polar code constructions proposed by the authors for deterministic broadcast channels, two theorems are introduced in the present paper for noisy two-user broadcast channels. The theorems establish polar code constructions for two important ...

2013

Proof of the Outage Probability Conjecture for MISO Channels

Emmanuel Abbé, Emre Telatar

It is conjectured that the covariance matrices minimizing the outage probability under a power constraint for multiple-input multiple-output channels with Gaussian fading are diagonal with either zeros or constant values on the diagonal. In the multiple-in ...

Institute of Electrical and Electronics Engineers2013

Adaptive sensing using deterministic partial Hadamard matrices

Emmanuel Abbé, Emre Telatar, Saeid Haghighatshoar

This paper investigates the construction of determin- istic measurement matrices preserving the entropy of a random vector with a given probability distribution. In particular, it is shown that for a random vector with i.i.d. discrete components, this is a ...

Ieee2012