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Filtering of Spatial Bias and Noise Inputs by Spatially Structured Neural Networks

masuda{at}mist.i.u-tokyo.ac.jp Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Japan, and ERATO Aihara Complexity Modelling Project, Japan Science and Technology Agency, Tokyo, Japan

Masato Okada

okada{at}k.u-tokyo.ac.jp Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan, and Intelligent Cooperation and Control, PRESTO, JST, Japan

Kazuyuki Aihara

aihara{at}sat.t.u-tokyo.ac.jp Institute of Industrial Science, University of Tokyo, Tokyo, Japan, and ERATO Aihara Complexity Modelling Project, Japan Science and Technology Agency, Tokyo, Japan

With spatially organized neural networks, we examined how bias and noise inputs with spatial structure result in different network states such as bumps, localized oscillations, global oscillations, and localized synchronous firing that may be relevant to, for example, orientation selectivity. To this end, we used networks of McCulloch-Pitts neurons, which allow theoretical predictions, and verified the obtained results with numerical simulations. Spatial inputs, no matter whether they are bias inputs or shared noise inputs, affect only firing activities with resonant spatial frequency. The component of noise that is independent for different neurons increases the linearity of the neural system and gives rise to less spatial mode mixing and less bistability of population activities.