Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topos and Stacks of Deep Neural Networks   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). Semantic functioning of a network
is its ability to express theories in such a language for answering questions
in output about input data. Quantities and spaces of semantic information are
defined by analogy with the homological interpretation of Shannon's entropy
(P.Baudot and D.B. 2015). They generalize the measures found by Carnap and
Bar-Hillel (1952). Amazingly, the above semantical structures are classified by
geometric fibrant objects in a closed model category of Quillen, then they give
rise to homotopical invariants of DNNs and of their semantic functioning.
Intentional type theories (Martin-Loef) organize these objects and fibrations
between them. Information contents and exchanges are analyzed by Grothendieck's
derivators.

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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg