49 citations · 83 across the 11 of their papers we have counts for
12 papers
Logical Information Cells I
Jean-Claude Belfiore, Daniel Bennequin, Xavier Giraud
In this study we explore the spontaneous apparition of visible intelligible reasoning in simple artificial networks, and we connect this experimental observation with a notion of s…
Superfield equations in the Berezin-Kostant-Leites category
Michel Egeileh, Daniel Bennequin
Using the functor of points, we prove that the Wess-Zumino equations for massive chiral superfields in dimension 4|4 can be represented by supersymmetric equations in terms of supe…
Topos and Stacks of Deep Neural Networks
Jean-Claude Belfiore, Daniel Bennequin
Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos…
Extra-fine sheaves and interaction decompositions
Daniel Bennequin, Olivier Peltre, Grégoire Sergeant-Perthuis +1
We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which Čech cohomology in strictly positive degree vanishes. We prov…
A functional equation related to generalized entropies and the modular group
Daniel Bennequin, Juan Pablo Vigneaux
We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of…
Topological Information Data Analysis
Pierre Baudot, Monica Tapia, Daniel Bennequin +1
This paper presents methods that quantify the structure of statistical interactions within a given data set, and was first used in \cite{Tapia2018}. It establishes new results on t…