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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 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 ...
Chat Generative Pre-trained Transformer (ChatGPT) is currently a trending topic worldwide triggering extensive debate about its predictive power, its potential uses, and its wider implications. Recent publications have demonstrated that ChatGPT can correct ...
It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically to succeed in fin ...
ASSOC COMPUTING MACHINERY2022
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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
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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
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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 COMPUTER SOC2019
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the re-cent years in sparser regimes. Yet, the current techniques still require diverg-ing degrees in order to succe ...
INST MATHEMATICAL STATISTICS-IMS2023
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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 ...
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 ...
