Computation with sequences of neural assemblies

Assemblies are subsets of neurons whose coordinated excitation could represent the subject's thinking of an object, idea, episode, or word, and so they provide a promising basis for a theory of how neurons and synapses give rise to higher-level cognitive phenomena. This key role of assemblies was hypothesized by the pioneering work of Hebb, while progress in neural recording technology in recent years has allowed their existence to be experimentally verified. Recent studies have documented the creation and activation of assemblies of neurons in sequence, especially after being trained on tasks involving sequential decisions. Here we study the brain's mechanisms for creating and using assembly sequences in the recently developed Assembly Calculus (AC), a simple and well-defined model of computation in the brain. We show that (1) the repeated presentation of a sequence of stimuli leads to the creation of a sequence of corresponding assemblies; upon future presentation of any small contiguous sub-sequence of stimuli, the corresponding assemblies are activated and continue until the end of the sequence, (2) when the stimulus sequence is projected to two brain areas in a ``scaffold'', both memorization and recall are more efficient, giving rigorous backing to the cognitive phenomenon that memorization and recall are easier with scaffolded memories, (3) more generally, we demonstrate that assemblies can be linked to simulate an arbitrary finite state machine (FSM), thereby capturing the brain's ability to memorize algorithms. This also makes the AC capable of arbitrary computation simply by the presentation of a suitable stimulus sequence, without explicit control commands. These findings provide a theoretical explanation at the neuronal level of complex phenomena such as rat learning behavior and human sequence memorization, as well as a concrete hypothesis as to how the brain's remarkable computational abilities could be realized.