Bridging the Gap Between Neurons and Cognition Through Assemblies of Neurons.

During recent decades, our understanding of the brain has advanced dramatically at both the cellular and molecular levels and at the cognitive neurofunctional level; however, a huge gap remains between the microlevel of physiology and the macrolevel of cognition. We propose that computational models based on assemblies of neurons can serve as a blueprint for bridging these two scales. We discuss recently developed computational models of assemblies that have been demonstrated to mediate higher cognitive functions such as the processing of simple sentences, to be realistically realizable by neural activity, and to possess general computational power.

Brain computation by assemblies of neurons.

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.

A Model for Structured Information Representation in Neural Networks of the Brain.

Humans can reason at an abstract level and structure information into abstract categories, but the underlying neural processes have remained unknown. Recent experimental data provide the hint that this is likely to involve specific subareas of the brain from which structural information can be decoded. Based on this data, we introduce the concept of assembly projections, a general principle for attaching structural information to content in generic networks of spiking neurons. According to the assembly projections principle, structure-encoding assemblies emerge and are dynamically attached to content representations through Hebbian plasticity mechanisms. This model provides the basis for explaining a number of experimental data and provides a basis for modeling abstract computational operations of the brain.

An impossibility theorem for price-adjustment mechanisms.

We show that there is no discrete-time price-adjustment mechanism (any process that at each period looks at the history of prices and excess demands and updates the prices) such that for any market (a set of goods and consumers with endowments and strictly concave utilities) the price-adjustment mechanism will achieve excess demands that are at most an epsilon fraction of the total supply within a number of periods that is polynomial in the number of goods and 1/epsilon. This holds even if one restricts markets so that excess demand functions are differentiable with derivatives bounded by a small constant. For the convergence time to the actual price equilibrium, we show by a different method a stronger result: Even in the case of three goods with a unique price equilibrium, there is no function of epsilon that bounds the number of periods needed by a price-adjustment mechanism to arrive at a set of prices that is epsilon-close to the equilibrium.