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math.AT2021★ 4 cited
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…
math.AT2020★ 4 cited
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…