Statistical and dynamical properties of large cortical network models: insights into semantic memory and language

This thesis introduces several variants to the classical autoassociative memory model in order to capture different characteristics of large cortical networks, using semantic memory as a paradigmatic example in which to apply the results. Chapter 2 is devoted to the development of the sparse Potts model network as a simplification of a multi modular memory performing computations both at the local and the global level. If a network storing p global patterns has N local modules, each one active in S possible ways with a global sparseness a, and if each module is connected to cM other modules, the storage capacity scales like αc ≡ pmax /cM ∝ S 2 /a with logarithmic corrections. Chapter 3 further introduces adaptation and correlations among patterns, as a result of which a latching dynamics appears, consistent in the spontaneous hopping between global attractor states after an initial cue-guided retrieval, somehow similar to a free association process. The complexity of the latching series depends on the equilibrium between self-excitation of the local networks and global inhibition represented by the parameter U. Finally, Chapter 4 develops a consistent way to store and retrieve correlated patterns, which works as long as any statistical dependence between units can be neglected. The popularity of units must be introduced into the learning rule, as a result of which a new property of associative memories appears: the robustness of a memory is inverse to the information it conveys. As in some accounts of semantic memory deficits, random damage results in selective impairments, associated to the entropy measure Sf of each memory, since the minimum connectivity required to sustain its retrieval is, in optimal conditions, cM ∝ pSf , and still proportional to pSf but possibly with a larger coefficient in the general case. Present in the entire thesis, but specially in this last Chapter, the conjecture stating that autoassociative memories are limited in the amount of information stored per synapse results consistent with the results.