A formalisation of the neural assembly concept 1. Constraints on neural assembly size

Abstract. Hebb proposed the concept of a neural assembly distributed across cortical tissue as a model for representation of information in the cerebral cortex. Later developments of the concept highlight the need for overlapping membership between independent assemblies, and the spread of activity throughout the assembly once it is activated above a critical level (ignition). Formalisation of the neural assembly concept, especially in relation to quantitative data from the real cortex, is at a very early stage. We consider two constraints on neural assembly size: (1) if a neural assembly is too small the fraction of its neurons that need to be active to ignite the whole assembly becomes unrealistically large; (2) if assemblies in a block of cortical tissue become too large then the block becomes ‘unsafe’, that is, unwanted spread from an active assembly to overlapping ones becomes inevitable. We consider variations in three parameters: neuronal firing threshold; connection density; and the total number of assemblies stored in the block of cortical tissue. Given biologically plausible values for these parameters we estimate maximum assembly size compatible with ignitability of individual assemblies, low probability of unwanted spread to overlapping assemblies, and safe operation of the block as a whole.