Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hessian-information geometric formulation of a class of deterministic
  neural network models   In this paper a class of dynamical systems describing deterministic neural
network models are formulated from a viewpoint of differential geometry. This
class includes the Hopfield model and gradient systems, and is such that the
so-called activation functions induce information and Hessian geometries. In
this formulation, it is shown that the phase space compressibility of a
dynamical system belonging to this class is written in terms of the Laplace
operator defined on Hessian manifolds, where phase space compressibility is
associated with a volume-form of a manifold, and expresses how such a
volume-form is compressed along the vector field of a dynamical system. Since
the sigmoid function, as an activation function, plays a role in the study of
neural network models, such compressibility is explicitly calculated for this
case. Throughout this paper, the so-called dual coordinates known in
information geometry are explicitly used.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg