Finite connectivity attractor neural networks

2003/04/11 by B Wemmenhove, B. Wemmenhove, A C C Coolen +1 · 3 citations
Computer Science · Physics and Astronomy · #Neural Networks and Applications #Neural Networks and Reservoir Computing #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/36/37/302

published as J. Phys. A: Math. Gen. 36 (2003) 9617 · 17 pages, 4 figures

arxiv created 2003/04/11 · openalex publication_date 2003/09/02 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/30

Abstract

We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous.

Citations

• Attractor modulation and proliferation in (1 + ∞)-dimensional neural networks
• An Exactly Solvable Asymmetric Neural Network Model

Cited by

• Spin models on random graphs with controlled topologies beyond degree constraints
• Entropies of complex networks with hierarchically constrained topologies
• Phase transitions in the three-state Ising spin-glass model with finite connectivity