word

Cortical modules

Local attractor states

Global activity patterns

A simple semantic network (O’Kane & Treves, 1992)

Structured long-rangeconnectivity

“0” state included

Sparse global patterns

updated to remove the‘memory glass’ problem (Fulvi Mari & Treves, 1998)

Potts units with diluteconnectivity

S+1 Potts states

Sparse Potts patterns

Reduced to a Potts model (Kropff & Treves, 2005)

..but all cortical modulesshare the same organization…

pc C S 2 !! pc S ?!?!

Simulations which include a model of neuronal fatigueshow that the Potts semantic network

can hop from global attractor to global attractor:Latching dynamics

SimulationsSimulations which include a model of neuronal fatigue

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?

pc C S 2

Storage capacity (max p to allow cued retrieval)

a spontaneous transition to infinite recursion?

+L+Lp p

SC

pl S ?

Latching onset (min p to ensure recursive process)

AM AM

long-range conn (local conn )

semantics

semantics

G Elstonet al

determ dete

rmra

nd

rand

Latching may be a neural basis for infinite recursion only iftransition probabilities are structured,

so that dynamics are neither random not deterministic

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 ofFrontal Latching Networks with

N = 300 Potts unitsa = 0.25 sparse codingS = 3,4,5,7,10 + 1 statesC = 12,17,25,50,100 connectionsp = 25-400 patternsgenerated by 20 relevant factors

How to quantify retrieval ?and latching ?

Retrieval and latching appear to coexistonly above critical values of both C and S

Is that to FLNs a percolation phase transition?