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Potts units with dilute connectivity S+1 Potts states Sparse Potts patterns Reduced to a Potts model (Kropff & Treves, 2005) Structured long-range connectivity “0” state included Sparse global patterns updated to remove the ‘memory glass’ problem (Fulvi Mari & Treves, 1998) Cortical modules Local attractor states Global activity patterns A simple semantic network (O’Kane & Treves, 1992) ..but all cortical modules share the same organization… pc  C S 2 !! pc  S ?!?!

Simulations which include a model of neuronal fatigue Simulations show that the Potts semantic network can hop from global attractor to global attractor: Latching dynamics

Hauser, Chomsky & Fitch

if transition probabilities are structured, Latching dynamics, if transition probabilities are structured, might be a neural model for infinite recursion

Monkey recordings by Moshe Abeles et al

How might have a capacity for indefinite latching evolved? semantics  semantics  AM AM C S long-range conn  (local conn ) Storage capacity (max p to allow cued retrieval) pc  C S 2 Latching onset (min p to ensure recursive process) pl  S ? a spontaneous transition to infinite recursion?

G Elston et al

Latching may be a neural basis for infinite recursion only if transition probabilities are structured, so that dynamics are neither random not deterministic determ rand pl  S ? pc  C S 2 ? + we need to confirm the crucial quantitative relationships, e.g. that in a multi-factor coding model (with correlated patterns) Emilio Kropff has taken care of that (J Nat Comput, 2006)

Computer simulations of Frontal Latching Networks with N = 300 Potts units a = 0.25 sparse coding S = 3,4,5,7,10 + 1 states C = 12,17,25,50,100 connections p = 25-400 patterns generated by 20 relevant factors How to quantify retrieval ? and latching ?

Retrieval and latching appear to coexist only above critical values of both C and S Is that to FLNs a percolation phase transition?