Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractal Analysis of the Coupling Space of Feed-Forward Neural
  Networks   Random input patterns induce a partition of the coupling space of
feed-forward neural networks into different cells according to the generated
output sequence. For the perceptron this partition forms a random multifractal
for which the spectrum $f(\alpha)$ can be calculated analytically using the
replica trick. Phase transition in the multifractal spectrum correspond to the
crossover from percolating to non-percolating cell sizes. Instabilities of
negative moments are related to the VC-dimension.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph