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- W4378468532 abstract "Several authors have recently highlighted the need for a new dynamical paradigm in the modelling of brain workings and evolution. In particular, the models should include the possibility of dynamic synaptic weights $T_{ij}$ in the neuron--neuron interaction matrix, radically overcoming the classical Hopfield setting. Krotov and Hopfield proposed a non constant, still symmetric model, leading to a vector field describing a gradient type dynamics and then including a Lyapunov--like energy function. In this note, we firstly will detail the general condition to produce a Hopfield like vector field of gradient type obtaining, as a particular case, the Krotov-Hopfield condition. Secondly, we abandon the symmetry because of two relevant physiological facts: (1) the actual neural connections have a marked directional character and (2) the gradient structure deriving from the symmetry forces the dynamics always towards stationary points, prescribing every pattern to be recognized. We propose a novel model including a set limited but varying controls $|xi_{ij}|leq K$ used for correcting a starting constant interaction matrix, $T_{ij}=A_{ij}+xi_{ij}$. Besides, we introduce a reasonable family of controlled variational functionals to be optimized. This allows us to reproduce the following three possible outcomes when submitting a pattern to the learning system. If (1) the dynamics leads to an already existing stationary point without activating the controls, the system has emph{recognized} an existing pattern. If (2) a new stationary point is reached by the activation of controls, then the system has emph{learned} a new pattern. If (3) the dynamics is unable to reach neither existing or new stationary points, then the system is unable to recognize or learn the pattern submitted. A further feature (4), appears to model emph{forgetting and restoring} memory." @default.
- W4378468532 created "2023-05-27" @default.
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- W4378468532 date "2023-05-11" @default.
- W4378468532 modified "2023-09-25" @default.
- W4378468532 title "Optimal Control Model for Brain Memory Working" @default.
- W4378468532 doi "https://doi.org/10.48550/arxiv.2305.14360" @default.
- W4378468532 hasPublicationYear "2023" @default.
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