J. Phys. France 51, 1403-1413 (1990)
DOI: 10.1051/jphys:0199000510130140300

Landscape statistics of the binary perceptron

J.F. Fontanari et R. Köberle

Instituto de Fisica e Quimica de São Carlos, Universidade de São Paulo, 13560 São Carlos SP, Brasil

Abstract
The landscape of the binary perceptron is studied by Simulated Annealing, exhaustive search and performing random walks on the landscape. We find that the number of local minima increases exponentially with the number of bonds, becoming deeper in the vicinity of a global minimum, but more and more shallow as we move away from it. The random walker detects a simple dependence on the size of the mapping, the architecture introducing a nontrivial dependence on the number of steps.

PACS
8710 - General theory and mathematical aspects.
0540 - Fluctuation phenomena, random processes, noise, and Brownian motion.
0705M - Neural networks, fuzzy logic, artificial intelligence.

Key words
neural nets -- random processes