Brain computation by assemblies of neurons

Abstract

Significance Our expanding understanding of the brain at the level of neurons and synapses, and the level of cognitive phenomena such as language, leaves a formidable gap between these two scales. Here we introduce a computational system which promises to bridge this gap: the Assembly Calculus. It encompasses operations on assemblies of neurons, such as project, associate, and merge, which appear to be implicated in cognitive phenomena, and can be shown, analytically as well as through simulations, to be plausibly realizable at the level of neurons and synapses. We demonstrate the reach of this system by proposing a brain architecture for syntactic processing in the production of language, compatible with recent experimental results.

A Biologically Plausible Parser

“…These operations are realistic in two orthogonal senses: first, they correspond to behaviors of assemblies that were either observed in experiments, or are helpful in explaining other experiments. Second, they provably correspond (they "compile down") to the activity of individual neurons and synapses; in Papadimitriou et al (2020), this correspondence is proven both mathematically and through simulations. It is hypothesized in Papadimitriou et al (2020) that the AC may underlie high-level cognitive functions.…”

“…Second, they provably correspond (they "compile down") to the activity of individual neurons and synapses; in Papadimitriou et al (2020), this correspondence is proven both mathematically and through simulations. It is hypothesized in Papadimitriou et al (2020) that the AC may underlie high-level cognitive functions. In particular, in the discussion section it is proposed that one particular operation of the AC called merge may play a role in the generation of sentences.…”

“…Assemblies can, through their near-simultaneous excitation, represent an object, episode, word or idea. It is shown in Papadimitriou et al (2020) that assemblies are an emergent property of the dynamical system under conditions (a) -(d) above, both in theory and in simulations.…”

“…Very recently, a computational model of brain function, the Assembly Calculus (AC), has been proposed (Papadimitriou et al, 2020). The AC describes a dynamical system involving the following parts and properties, well attested in the neuroscience literature: a) brain areas with random connections between neurons; b) a simple linear model of neuronal inputs; c) inhibition within each area such that the top k most activated neurons fire; d) a simple model of Hebbian plasticity, whereby the strength of synapses increase as neurons fire.…”

“…Note that, regarding the soundness of the AC, what has been established through mathematical proof is that AC operations work correctly with high probability, where the underlying probabilistic event is the creation of the random connectome. So far, the simulation experiments conducted with the AC have demonstrated that individual commands of the AC, or short sequences thereof, can be successfully and reliably implemented in a simulator (Papadimitriou et al, 2020). Do such simulations scale?…”