bioRxiv2019
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. Operations on assemblies include: projection (duplicating an assembly by creating a new assembly in a downstream brain area); reciprocal projection (a variant of projection also entailing synaptic connectivity from the newly created assembly to the original one); association (increasing the overlap of two assemblies in the same brain area to reflect cooccurrence or similarity of the corresponding concepts); merge (creating a new assembly with ample synaptic connectivity to and from two existing ones); and pattern-completion (firing of an assembly, with some probability, in response to the firing of some but not all of its neurons). Our analytical results establishing the plausibility of these operations are proved in a simplified mathematical model of cortex: a finite set of brain areas each containing n excitatory neurons, with random connectivity that is both recurrent (within an area) and afferent (between areas). Within one area and at any time, only k of the n neurons fire -- an assumption that models inhibition and serves to define both assemblies and areas -- while synaptic weights are modified by Hebbian plasticity, as well as homeostasis. Importantly, all neural apparatus needed for the functionality of the assembly operations is created on the fly through the randomness of the synaptic network, the selection of the k neurons with the highest synaptic input, and Hebbian plasticity, without any special neural circuits assumed to be in place. 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. As with high-level programming languages, a computation in the Assembly Calculus (that is, a coherent sequence of assembly operations accomplishing a task) can ultimately be reduced -- "compiled down" -- to computation by neurons and synapses; however, it would be far more cumbersome and opaque to represent the same computation that way. 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.