Abstract
Assemblies are large populations of neurons believed to imprint memories, concepts, words, and other cognitive information. We identify a repertoire of operations on assemblies. These operations correspond to properties of assemblies observed in experiments, and can be shown, analytically and through simulations, to be realizable by generic, randomly connected populations of neurons with Hebbian plasticity and inhibition. Assemblies and their operations constitute a computational model of the brain which we call the Assembly Calculus, occupying a level of detail intermediate between the level of spiking neurons and synapses and that of the whole brain. The resulting computational system can be shown, under assumptions, to be, in principle, capable of carrying out arbitrary computations. We hypothesize that something like it may underlie higher human cognitive functions such as reasoning, planning, and language. In particular, we propose a plausible brain architecture based on assemblies for implementing the syntactic processing of language in cortex, which is consistent with recent experimental results.