A Calculus for Brain Computation

Do brains compute? How do brains learn? How are intelligence and language achieved in the human brain? In this pursuit, we develop a formal calculus and associated programming language for brain computation, based on the assembly hypothesis, first proposed by Hebb: the basic unit of memory and computation in the brain is an assembly, a sparse distribution over neurons. We show that assemblies can be realized efficiently and neuroplausibly by using random projection, inhibition, and plasticity. Repeated applications of this RP&C primitive (random projection and cap) lead to (1) stable assembly creation through projection; (2) association and pattern completion; and finally (3) merge, where two assemblies form a higher-level assembly and, eventually, hierarchies. Further, these operations are composable, allowing the creation of stable computational circuits and structures. We argue that this functionality, in the presence of merge in particular, might underlie language and syntax in humans.

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