ABSTRACT
A stochastic neural network, using the ordinary laws of thermodynamics, can develop a representation of what might be called a state of cognitive equilibrium (Hutton, 1991). If it is assumed that there is a quanta] nature to behavior (and hence cognition) and that inputs are logarithmically transformed, three important and not obviously related psychological laws, usually treated as empirical generalizations, can be derived from first principles. Steven’s Law relates the subjective impression of a stimulus to its objective magnitude. Herrnstein’s equation relates absolute response rate to absolute reinforcement rate. The generalized matching law makes quantitative predictions about choice by assuming that a power law describes the relationship between behavioral states and relative value of alternatives. Assume a neural net with symmetric weights and a stochastic update rule. This results in relative output probabilities that are determined by a Boltzmann distribution. If inputs are logarithmically transformed, then the generalized matching law and Steven’s Law can be derived from the network equations. Assuming limited capacity, Herrnstein’s equation falls out. The results suggest heretofore unreported links between some apparently unrelated psychological laws, and show the importance of thermodynamic principles to states of cognitive/behavioral equilibria. They also show a plausible mechanism for the emergence of power law relationships that is not in any way restricted to treatments of cognitive and other behavioral states.
