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Poster B98 in Poster Session B - Thursday, August 8, 2024, 1:30 – 3:30 pm, Johnson Ice Rink
Emergent symmetry in a finite model of navigational neurons
Vadim Weinstein1 (), Filip Georgiev1, Kalle G. Timperi1, Nicoletta Prencipe1, Steven M. LaValle1; 1Center for Ubiquitous Computing, Faculty of Information Technology and Electrical Engineering, University of Oulu
Consider an agent moving in the n-dimensional integer lattice. We model a neuron of this agent as a finite transition system and show, using a pumping lemma type of argument, that a grid cell-like behavior emerges under very mild assumptions. If there is one location in the environment which is reliably recognized by the neuron, then there is a ``grid'' of locations which are indistinguishable from the point of view of that neuron. By a grid we mean a finite union of cosets of a full-rank subgroup of the lattice. We propose that this may shed light on the possible origins of grid cells, because there is an evolutionary pressure to recognize when the organism has returned to a given location.
Keywords: grid cells finite automata information transition systems emergence