Asymmetrically extremely dilute neural networks with non-trivial\n dynamics

2004/04/30 by J. P. L. Hatchett, Hatchett, J. P. L., A C C Coolen +1
Computer Science · Neuroscience · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Neural Networks and Applications #Neural dynamics and brain function #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.cond-mat/0404742

openalex publication_date 2004/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study graded response attractor neural networks with asymmetrically\nextremely dilute interactions and Langevin dynamics. We solve our model in the\nthermodynamic limit using generating functional analysis, and find (in contrast\nto the binary neurons case) that even in statics one cannot eliminate the\nnon-persistent order parameters. The macroscopic dynamics is driven by the\n(non-trivial) joint distribution of neurons and fields, rather than just the\n(Gaussian) field distribution. We calculate phase transition lines and present\nsimulation results in support of our theory.\n

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