Designing the Dynamics of Spiking Neural Networks

Abstract

Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic patterns of spikes that are precisely timed. We develop an analytical method to find the set of all networks exhibiting a predefined pattern dynamics. Such patterns may be arbitrarily long and of complicated temporal structure. We point out that the same pattern can exist in very different networks and have different stability properties.

arXiv comment4 pages, 3 figures

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• Inferring Network Topology from Complex Dynamics
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• On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses
• Designing Complex Networks
• Bounding network spectra for network design
• Reconstructing networks of pulse-coupled oscillators from spike trains
• Inferring network connectivity from event timing patterns
• How Chaotic is the Balanced State?
• Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks
• Hysteretic percolation from locally optimal individual decisions
• The winner takes it all -- How to win network globalization
• Smooth Exact Gradient Descent Learning in Spiking Neural Networks
• Storage capacity of phase-coded patterns in sparse neural networks
• Reconfigurable Computation in Spiking Neural Networks
• Partially unstable attractors in networks of forced integrate-and-fire oscillators