q-Maximum Entropy Distributions and Memory Neural Networks

摘要

q-Maximum Entropy (q-MaxEnt) distributions optimizing the S_q, power-law entropic functionals are at the core of the nonextensive thermostatistical formalism. This formalism has been increasingly applied to the description of diverse complex systems in physics, biology, economics, and other fields. Previous work on computational neural models for mental phenomena, such as neurosis, creativity, and the interplay between consciousness and unconsciousness, suggests that q-MaxEnt distributions may be relevant for the study of neural models for these processes. Evidence for q-MaxEnt distributions arises in connection with models of associative memory, which constitute a key ingredient in the theoretical analysis of the alluded mental phenomena. In the present contribution, we compare two possible dynamical mechanisms leading to q-MaxEnt distributions in memory neural networks, when these are modeled by linear or non-linear deformed Fokker-Planck equations. Our joint analysis of these two formalisms (that have been treated separately in the literature) allow us to identify some general features of these approaches that clarify and differentiate their underlying physical basis.