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Kinetic Morphogenesis of a Multilayer Perceptron

We introduce a morphogenesis paradigm for a neural network where neurons are allowed to move autonomously in a topological space to reach suitable reciprocal positions under an informative perspective. To this end, a neuron is attracted by the mates which are most informative and repelled by those which are most similar to it. We manage the neuron motion with a Newtonian dynamics in a subspace of a framework where topological coordinates match with those reckoning the neuron connection weights. As a result, we have a synergistic plasticity of the network which is ruled by an extended Lagrangian where physics components merge with the common error terms. With the focus on a multilayer perceptron, this plasticity is operated by an extension of the standard back-propagation algorithm which proves robust even in the case of deep architectures. We use two classic benchmarks to gain some insights on the morphology and plasticity we are proposing.