In this paper, we study memory iteration where the updating considers a longer history of each site and the set of interaction matrices is quasi-palindromic. For parallel and sequential iterations with memory, we define Lyapunov functional which permits us to characterize the periods behaviour and explicitly bounds the transient lengths of quasi-palindromic neural networks. For these networks, the dynamics are robust with respect to a class of small changes of the interactions matrices.

http://users.ictp.it/~pub_off/preprints-sources/2007/IC2007107P.pdf

United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS DYNAMICAL BEHAVIOUR OF QUASI-PALINDROMIC NEURAL NETWORKS ITERATED WITH MEMORY

We study memory iteration where the updating consider a longer history of each site and the set of interaction matrices is palindromic. We analyze two different ways of updating the networks: parallel iteration with memory and sequential iteration with memory that we introduce in this paper. For parallel iteration, we define Lyapunov functional which permits us to characterize the periods behaviour and explicitely bounds the transient lengths of neural networks iterated with memory. For sequential iteration, we use an algebraic invariant to characterize the periods behaviour of the studied model of neural computation.

International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS DYNAMICAL BEHAVIOUR OF NEURAL NETWORKS ITERATED WITH MEMORY

We study the sequences generated by neuronal recurrence equations of the form x(n) = 1[ P k=1 ajx(n − j) − θ], where k is the size of memory (k represents the number of previous states x(n − 1), x(n − 2), . . . , x(n − k) which intervene in the calculation of x(n)). We are interested in the number of steps (transient length) from an initial configuration to the cycle. We propose a method of construction of transient from a cycle generated by neuronal recurrence equation. We apply this method to build a neuronal recurrence equation with inhibitory memory of size (s+ 1)6m, whose dynamics contains an evolution of transient length (s+1) ×(5m+2 + lcm(p0, p1, . . . , ps−1,3m − 1)) and a cycle of length (s + 1) × lcm(p0, p1, . . . , ps−1,2m + 1) where lcm denotes the least common multiple, and p0, p1, . . . , ps−1 are prime numbers lying between 2m and 3m.

/pdf/international-atomic-energy-agency-the-abdus-salam-nbgut37mo1.pdf

International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS METHOD OF CONSTRUCTION OF TRANSIENT FROM A CYCLE OF NEURONAL RECURRENCE EQUATION

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International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS DYNAMICAL BEHAVIOUR OF NEURAL NETWORKS ITERATED WITH MEMORY

International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS METHOD OF CONSTRUCTION OF TRANSIENT FROM A CYCLE OF NEURONAL RECURRENCE EQUATION