Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Deterministic Learning Dynamics in Large Neural Networks due to
  Structural Data Bias   We study the dynamics of on-line learning in large perceptrons, for the case
of training sets with a structural bias of the input vectors, by deriving exact
and closed macroscopic dynamical laws using non-equilibrium statistical
mechanical tools. In sharp contrast to the more conventional theories developed
for homogeneously distributed or only weakly biased data, these laws are found
to describe a non-trivial and persistently non-deterministic macroscopic
evolution, and a generalisation error which retains both stochastic and
sample-to-sample fluctuations, even for infinitely large networks. Furthermore,
for the standard error-correcting microscopic algorithms (such as the
perceptron learning rule) one obtains learning curves with distinct
bias-induced phases. Our theoretical predictions find excellent confirmation in
numerical simulations.

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The categories of this paper are: funct-an
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics