In this lecture, we introduce thinking about computation from a complex systems perspective. This transition is motivated by thinking about physiological details of neuron-to-neuron communication (e.g., different synapse types, a variety of neurotransmitters, neuromodulatory feedback from other parts of the brain, neuropharmacology) are much more well understood at the local level than they are at the level of emergent cognitive phenomena, and none of these details are currently being incorporated into neuromorphic approaches to artificial cognition. Complex systems methods (which are methods applied to systems where local-level interactions are easy to describe but large-scale, system-level phenomena emerge non-trivially from those interactions) provide one perspective to better understanding such emergence.
We then introduce Interacting Particle Systems (IPS), for which cellular automata (and both artificial neural networks, ANNs, and spiking neural networks, SNNs) can be viewed as a special case. Before jumping into cellular automata in the next lecture, we close this lecture discussing the "voter model", which is a model of neutral evolution (i.e., evolution by drift alone with no selective/fitness effects). Asking whether the voter model reaches fixation is equivalent to asking whether the computational system of interacting particles reach consensus. The answer to this requires using a dual, time-reversed system of coalescing Markov chains akin to doing contact tracing in an epidemiological system. The result (making use of Polya's recurrence theorem) is that consensus (fixation) will occur for 1 or 2 dimensions but will not always occur (i.e., will fail with non-zero probability) in 3 dimensions or higher.
Whiteboard notes for this lecture can be found at:
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