1. word

2. 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 ?!?!

3. 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

4. Hauser, Chomsky & Fitch

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

6. Monkey recordings by Moshe Abeles et al

7. 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?

8. G Elston
et al

10. 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)

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

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