Interpreting polychronization through the lens of tropical geometry

Timing information of neural spikes is thought to be one of many ways in which the brain encodes information. In the temporal coding regime, synaptic delays become crucial for understanding cognitive dynamics, and spiking neural networks with nontrivial synaptic delays are known to express certain complex behaviors such as polychronization. In this talk, we explore the link between such delay networks and a field of mathematics called tropical algebra, which has found applications in fields from optimization and control to field theory. We demonstrate that certain classes of polychronous patterns in spiking integrate-and-fire neural networks are in fact vertices of tropical eigenspaces, and consider what other lessons tropical geometry may have to tell us about temporal dynamics in the brain and in temporally-coded neuromorphic systems.