• Corpus ID: 235658960

Topos and Stacks of Deep Neural Networks

@article{Belfiore2021ToposAS,
  title={Topos and Stacks of Deep Neural Networks},
  author={Jean-Claude Belfiore and Daniel Bennequin},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.14587}
}
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… 

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