UNSTABLE SOLUTIONS OF NON-AUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS

Changes in neural connectivity are thought to underlie the most permanent forms of memory in the brain. We consider two models, derived from the clusteron, to study this method of learning. The models show a direct relationship between the speed of memory acquisition and the probability of forming appropriate synaptic connections. Moreover, the strength of learned associations grows with the number of fibers that have taken part in the learning process. We provide simple and intuitive explanations of these two results by analyzing the distribution of synaptic activations. The obtained insights are then used to extend the model to perform novel tasks: feature detection, and learning spatio-temporal patterns. We also provide an analytically tractable approximation to the model to put these observations on a firm basis. The behavior of both the numerical and analytical models correlate well with experimental results of learning tasks which are thought to require a reorganization of neuronal networks.

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