Abstract
Much of our recent work regards the development of schematic, neurocomputational models based on memory associativity to describe some processes associated with basic structures of mental functioning, such as neurosis, creativity, consciousness/unconsciousness, and psychoses. We have emphasized associative memory mechanisms, since they are central in the description of these processes by psychodynamical theories. In memory neural networks, such as the Hopfield or Boltzmann Machine models, the symmetry of synaptic connections is a condition for the existence of stationary states, although this assumption is biologically unrealistic. Many efforts to model stationary states of networks with asymmetric weights are mathematically complex and can usually be applied only to specific cases. We thus further explore a possible new approach to the asymmetry problem, based on studies of some characteristics of the behavior of these networks, which may be modeled by the Fokker-Planck formalism. Besides considering asymmetric interactions, we also relaxed other symmetries of our previous models, enriching the concomitant dynamics. Among other things, we identified the presence of limit cycles.
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We acknowledge financial support from the Brazilian National Research Council (CNPq), the Rio de Janeiro State Research Foundation (FAPERJ) and the Brazilian agency which funds graduate studies (CAPES).
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de Luca, V.T.F., Wedemann, R.S., Plastino, A.R. (2018). Neuronal Asymmetries and Fokker-Planck Dynamics. In: Kůrková, V., Manolopoulos, Y., Hammer, B., Iliadis, L., Maglogiannis, I. (eds) Artificial Neural Networks and Machine Learning – ICANN 2018. ICANN 2018. Lecture Notes in Computer Science(), vol 11141. Springer, Cham. https://doi.org/10.1007/978-3-030-01424-7_69
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