On the parallel dynamics of theQ-state Potts andQ-Ising neural networks

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“…and where we recall that T j is the part of the tree connected to neuron j, we find using standard signal-to-noise techniques (see, e.g., [6], [11])…”

“…Compared with the asymmetrically diluted model [11] the architecture is still a local Cayley-tree but no longer directed and in the limit N → ∞ the probability that the number of connections T i = {j ∈ Λ|c ij = 1} giving information to the site i ∈ Λ is still a Poisson distribution with mean C = E[|T i |]. Thereby it is assumed that C ≪ log N and in order to get an infinite average connectivity allowing to store infinitely many patterns p one also takes the limit C → ∞ and defines the capacity α by p = αC.…”

Mutual information of sparsely coded associative memory with self-control and ternary neurons

“…This allows us to derive the first time-step in the evolution of the network. For diluted architectures this first step dynamics describes the full time evolution and we arrive at (Derrida et al, 1987;Yedidia, 1989;Bollé et al, 1993)…”

Categorization by a three-state attractor neural network

“…The dynamics of this model is then studied following standard methods involving a signal-to-noise analysis (see, e.g., [19], [20], [21]). At this point we recall that it is justified to first dilute the system by taking the limit N → ∞ and second, in the diluted system, to apply the law of large numbers (LLN) and the central limit theorem (CLT) by taking the limit C → ∞.…”

“…In order to measure the quality of retrieval of the examples we introduce the Hamming distance between the stored example and the microscopic state of the network [20] …”