Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A gradient system on the quantum information space realizing the
  averaged learning equation of Hebb type   The averaged learning equation (ALEH) applicable to the principal component
analyzer is studied from both quantum information geometry and dynamical system
viewpoints. On the quantum information space (QIS), the space of regular
density matrices endowed with the quantum SLD-Fisher metric, a gradient system
is given as an extension of the ALEH; on the submanifold, consisting of the
diagonal matrices, of the QIS, the gradient flow coincides with the ALEH up to
a local diffeomorphism.

34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess