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Noemie Combe

Publications and source records attributed to Noemie Combe.

5 recordsLinked to original sources
arXiv2022

Moufang Patterns and Geometry of Information

Technology of data collection and information transmission is based on various mathematical models of encoding. The words "Geometry of information" refer to such models, whereas the words "Moufang patterns" refer to various sophisticated symmetries appearing naturally in such models. In this paper we show that the symmetries of spaces of probability distributions, endowed with their canonical Riemannian metric of information geometry, have the structure of a commutative Moufang loop. We also show that the F-manifold structure on the space of probability distribution can be described in terms of differential 3-webs and Malcev algebras. We then present a new construction of (noncommutative) Moufang loops associated to almost-symplectic structures over finite fields, and use then to construct a new class of code loops with associated quantum error-correcting codes and networks of perfect tensors.

cs.IT↗
arXiv2021

Quantum Operads

The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more sophisticated: quasigroups, loops, quantum groups, ... In this paper, we introduce and study quantum symmetries of very general categorical structures: operads. Its initial motivation were spaces of probability distributions on finite sets. We also investigate here how structures of quantum information, such as quantum states and some constructions of quantum codes are algebras over operads.

math.QA↗
arXiv2021

Geometry of Information: classical and quantum aspects

In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic enrichments.

cs.IT↗
arXiv2020

Mind2Mind : transfer learning for GANs

Training generative adversarial networks (GANs) on high quality (HQ) images involves important computing resources. This requirement represents a bottleneck for the development of applications of GANs. We propose a transfer learning technique for GANs that significantly reduces training time. Our approach consists of freezing the low-level layers of both the critic and generator of the original GAN. We assume an autoencoder constraint in order to ensure the compatibility of the internal representations of the critic and the generator. This assumption explains the gain in training time as it enables us to bypass the low-level layers during the forward and backward passes. We compare our method to baselines and observe a significant acceleration of the training. It can reach two orders of magnitude on HQ datasets when compared with StyleGAN. We prove rigorously, within the framework of optimal transport, a theorem ensuring the convergence of the learning of the transferred GAN. We moreover provide a precise bound for the convergence of the training in terms of the distance between the source and target dataset.

cs.LG↗