Energy functional and fixed points of a neural network
Leonid B. Litinskii (Institute for High Pressure Physics Russian, Academy of Sciences)
TL;DR
This paper investigates the properties of energy functionals and fixed points in neural network dynamic systems, analyzing how connection matrices influence system stability and fixed point structure.
Contribution
It characterizes conditions on connection matrices that align fixed points with local energy minima and examines the impact of diagonal elements on fixed point configurations.
Findings
Connection matrix properties determine fixed point and energy minimum coincidence.
Diagonal elements of the connection matrix influence the structure of fixed points.
The study provides criteria for stability in neural network dynamics.
Abstract
A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the dynamic system with the set of the local minima of the energy functional, have been determined. The influence of the connection matrix diagonal elements on the structure of the fixed points set has been investigated.
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Taxonomy
TopicsNeural Networks and Applications