Topos and Stacks of Deep Neural Networks

Understand

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.

• Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks.
• This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints.
• The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard).