Finite Connectivity Attractor Neural Networks

Details Finite Connectivity Attractor Neural Networks Finite Connectivity Attractor Neural Networks

2003-04-11

arxiv.org/abs/cond-mat/0304282v1

J. Phys. A: Math. Gen. 36 (2003) 9617

Physics

Condensed Matter

Disordered Systems and Neural Networks

17 pages, 4 figures

Scientific paper

10.1088/0305-4470/36/37/302

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 (RS) 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.

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