Discrete Dynamics in Nature and Society
Volume 3 (1999), Issue 1, Pages 43-49

Cognition: Differential-geometrical view on neural networks

S. A. Buffalov

Radio-physical Department, Tomsk State University, Lytkina 24-109, Tomsk 634034, Russia

Received 4 February 1999

Copyright © 1999 S. A. Buffalov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A neural network taken as a model of a trainable system appears to be nothing but a dynamical system evolving on a tangent bundle with changeable metrics. In other words to learn means to change metrics of a definite manifold.