126 citations · 555 across the 57 of their papers we have counts for
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Entropic matroids and their representation
Emmanuel Abbe, Sophie Spirkl
This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider -entropic matroi…
Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Nets
Amir R. Asadi, Emmanuel Abbe
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing…
Subadditivity Beyond Trees and the Chi-Squared Mutual Information
Emmanuel Abbe, Enric Boix-Adserà
In 2000, Evans et al. [Eva+00] proved the subadditivity of the mutual information in the broadcasting on tree model with binary vertex labels and symmetric channels. They raised th…
Recursive projection-aggregation decoding of Reed-Muller codes
Min Ye, Emmanuel Abbe
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 cos…
Reed-Muller codes polarize
Emmanuel Abbe, Min Ye
Reed-Muller (RM) codes and polar codes are generated by the same matrix but using different su…