Publications by Emmanuel Abbé

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Reed-Muller (RM) codes have undergone significant analytical advancements over the past decade, particularly for binary memoryless symmetric (BMS) channels. We extend the scope of RM codes development and analysis to multiple-access channels (MACs) and quantum Pauli channels, leveraging a unified approach. Specifically, we first derive the achievable rate region for RM codes on so-called Q-MACs, a class of MACs with additive correlated noise. This is achieved via a generalization of the bending and boosting

L’intelligence artificielle (IA) n’est plus seulement un terme à la mode. Elle devient une partie intégrante de notre vie quotidienne et de notre pratique médicale. Grâce aux avancées majeures des 5 dernières années, l’IA ouvre de nouvelles voies pour aider à améliorer la prévention cardiovasculaire. Cet article en détaille deux aspects : a) aider le patient à gérer ses facteurs de risque cardiovasculaire et son éducation médicale de manière plus autonome et b) aider les cliniciens à améliorer les pratiques

This paper investigates polar coding schemes achieving capacity for the AWGN channel. The approaches using a multiple access channel with a large number of binary-input users and a single-user channel with a large prime-cardinality input are compared with respect to complexity attributes. The problem of finding discrete approximations to the Gaussian input is then investigated, and it is shown that a quantile quantizer achieves a gap to capacity which decreases like 1/q (where q is the number of constellati

This paper shows that a class of codes such as Reed-Muller (RM) codes have vanishing bit-error probability below capacity on symmetric channels. The proof relies on the notion of "camellia codes": a class of symmetric codes decomposable into "camellias", i.e., set systems that differ from sunflowers by allowing for scattered petal overlaps. The proof then follows from a boosting argument on the camellia petals with second moment Fourier analysis. For erasure channels, this gives a self-contained proof of th

Invasive Coronary Angiography (ICA) is the clinical gold standard for the assessment of coronary artery disease. However, its interpretation remains subjective and prone to intra- and inter-operator variability. In this work, we introduce ODySSeI: an Open-source end-to-end framework for automated Detection, Segmentation, and Severity estimation of lesions in ICA images. ODySSeI integrates deep learning-based lesion detection and lesion segmentation models trained using a novel Pyramidal Augmentation Scheme

The r-th power of a graph modifies a graph by connecting every vertex pair within distance r. This paper gives a generalization of the Alon-Boppana Theorem for the r-th power of graphs, including irregular graphs. This leads to a generalized notion of Ramanujan graphs, those for which the powered graph has a spectral gap matching the derived Alon-Boppana bound. In particular, we show that certain graphs that are not good expanders due to local irregularities, such as Erdos-Renyi random graphs, become almost

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 ...

The goal of this work is to investigate the ability of transfer learning (TL) and multitask learning (MTL) algorithms to predict tasks related to myocardial infarction (MI) in a small-data regime, leveraging a larger dataset of haemodynamic targets. The da ...

This paper analyzes the use of non-Gaussian input distributions over the Gaussian interference channel. It has been recently proved that the iid Gaussian code ensemble together with a decoder that treats interference as noise is sum-capacity achieving, if the interference is below a threshold. We show that, when the decoder treats interference as noise, and when the interference is above a threshold, the iid Gaussian ensemble can be strictly improved upon. In the block synchronous setting, the improvement i

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 ...

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 ...

Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we address a similar question, but with respect to a universal generalized linear decoder. We look for the best collection of finitely many a posteriori metrics, to maximize the worst case mismatched mutual information achieved by decoding with these metrics (instead of an optim

Purpose: This study aimed to evaluate the efficacy of the Chat Generative Pre-trained Transformer (ChatGPT) in guiding the need for invasive coronary angiography (ICA) in high-risk non-ST-elevation (NSTE) acute coronary syndrome (ACS) patients based on bot ...

BackgroundAngiographic parameters can facilitate the risk stratification of coronary lesions but remain insufficient in the prediction of future myocardial infarction (MI).AIMSWe compared the ability of humans, angiographic parameters and deep learning (DL ...

The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper provides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating

This talk shows how computational lower bounds in learning, which allow to show failure at learning certain function classes due to computational constraints, can be derived using information-theoretic arguments and inequalities. In particular, it is shown that GDbased deep learning cannot learn with polynomial parameters certain function classes that can be learned efficiently with other non-GD based algorithms. Joint work with C. Sandon (MIT).

This paper introduces the notion of "Initial Alignment" (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent on a fu ...

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 ...

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 ...

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 ...

Emmanuel Abbé

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Reed-Muller Codes for Quantum Pauli and Multiple Access Channels

Comment l’intelligence artificielle peut-elle améliorer la prévention cardiovasculaire ?

Polar coding schemes for the AWGN channel

Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting

ODySSeI: An Open-Source End-to-End Framework for Automated Detection, Segmentation, and Severity Estimation of Lesions in Invasive Coronary Angiography Images

An Alon-Boppana theorem for powered graphs and generalized Ramanujan graphs

Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Can Knowledge Transfer Techniques Compensate for the Limited Myocardial Infarction Data by Leveraging Haemodynamics? An in silico Study

Coding along Hermite polynomials for interference channels

Polarization in Attraction-Repulsion Models

Proof of the Outage Probability Conjecture for MISO Channels

Universal a posteriori metrics game

Assessing the need for coronary angiography in high-risk non-ST-elevation acute coronary syndrome patients using artificial intelligence and computed tomography

Deep learning-based prediction of future myocardial infarction using invasive coronary angiography: a feasibility study

Learning Sparse Graphons and the Generalized Kesten-Stigum Threshold

From Information Inequalities to Computational Lower Bounds in Learning

An Initial Alignment between Neural Network and Target is Needed for Gradient Descent to Learn

System and method for decoding reed-muller codes

Subadditivity Beyond Trees and the Chi-Squared Mutual Information

Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels