We will run through methods that quantify the statistical interactions structure within a given data set using the characterization of information theory in cohomology by finite methods, and provide their expression in term of statistical physic and machine learning. We will focus on how such model reconcile the main theories of consciousness (Integrated Information, Free energy principle, neural assemblies) and generalize Deep Neural Network with some applications to unsupervised and supervised learning on standard data set.

Pierre Baudot (a,c), in collaboration (in part) with Daniel Bennequin (b), Monica Tapia (c) , and Jean-Marc Goaillard (c)

a. Median Technologies, 06560 Valbonne, France

b. Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France

c. Inserm UNIS UMR1072 – Université Aix-Marseille, Marseille, France

Baudot P., Tapia M., Bennequin, D. , Goaillard J.M., Topological Information Data Analysis. 2019, Entropy, 21(9), 869

Baudot P., The Poincaré-Shannon Machine: Statistical Physics and Machine Learning aspects of Information Cohomology. 2019, Entropy , 21(9),

Baudot P., Elements of qualitative cognition: an Information Topology Perspective. Physics of Life Reviews . 2019. Extended version arXiv:1807.04520

Vigneaux, J.P. Topology of statistical systems: a cohomological approach to information theory. PhD thesis 2019

Baudot P., Bennequin D., The homological nature of entropy. Entropy, 2015, 17, 1-66; doi:10.3390.

Tapia M., Baudot P., Dufour M., Formizano-Treziny C., Temporal S., Lasserre M., Kobayashi K., Goaillard J.M.. Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons. Scientific Reports. 2018.