Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On variation of gradients of deep neural networks   We provide a theoretical explanation of the role of the number of nodes at
each layer in deep neural networks. We prove that the largest variation of a
deep neural network with ReLU activation function arises when the layer with
the fewest nodes changes its activation pattern. An important implication is
that deep neural network is a useful tool to generate functions most of whose
variations are concentrated on a smaller area of the input space near the
boundaries corresponding to the layer with the fewest nodes. In turn, this
property makes the function more invariant to input transformation. That is,
our theoretical result gives a clue about how to design the architecture of a
deep neural network to increase complexity and transformation invariancy
simultaneously.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an