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• W2170830619 abstract "Associative reconstruction of noisy data in a neural network can be accomplished by endowing a pattern to be memorized with a basin of attraction for the system's retrieval dynamics. ' If the dynamics is governed by a Lyapunov function, a simple intuitive understanding of the global computation becomes possible: The system performs a downhill motion in an energy landscape created by the stored information. For networks with static patterns, there is a Lyapunov function if the interactions between single neurons are instantaneous and mediated by symmetric couplings. Methods of equilibrium statistical mechanics may then be applied and permit a quantitative analysis of the network's performance in terms of the retrieval quality and storage capacity. The existence of a Lyapunov function is thus of great conceptual as well as technical importance. In general, external inputs to a neural network are not limited to static memories but provide information in both space and time. To code the temporal aspects of sequences of patterns to be learned, additional asymmetric couplings with transmission delays may be introduced. This approach can be generalized to networks with a broad distribution of signal delays where Hebb's neurophysiological principle for learning naturally leads to a joint representation of spatial and temporal information. However, no description in terms of a Lyapunov function has been given so far. In this Letter such a description is developed for a certain class of networks with transmission delays. We present a Lyapunov functional for the deterministic parallel dynamics, generalize the formalism of equilibrium statistical mechanics so as to deal with thermal noise in systems with delayed interactions, and, hence, make the domain of time-dependent phenomena accessible to powerful free-energy techniques. We follow Refs. 1-3 and model single neurons by Ising spins 5;, 1 ~i ~ N. They represent a firing state for 5; =+1 and a quiescent one for 5; = — 1. The neurons are connected by synapses with modifiable efficacies J;, (r). Here r denotes a fixed time delay for the information transport from j to i. We focus on a solitonlike propagation of neural signals, characteristic for the (axonal) transmission of action potentials, and consider a model where each pair of neurons is linked by several axons with delays 0~ ~~ r, „. External stimuli are fed into the system via two-state receptors cr; = + 1. The local fields (postsynaptic potentials) are then given by N max" @default.
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• W2170830619 date "1991-03-11" @default.
• W2170830619 modified "2023-10-18" @default.
• W2170830619 title "Statistical mechanics of temporal association in neural networks with transmission delays" @default.
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• W2170830619 doi "https://doi.org/10.1103/physrevlett.66.1370" @default.
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