Inference and learning in sparse systems with multiple states

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.056114· OSTI ID:21560287

Braunstein, A ^[1]; Ramezanpour, A; Zhang, P ^[2]; Zecchina, R ^[2]

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1. Human Genetics Foundation, Via Nizza 52, I-10126 Torino (Italy)
2. Politecnico di Torino, C.so Duca degli Abruzzi 24, I-10129 Torino (Italy)

We discuss how inference can be performed when data are sampled from the nonergodic phase of systems with multiple attractors. We take as a model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states. We also show how the inference results can be converted into a learning protocol for neural networks in which patterns are presented through weak external fields. The protocol is simple and fully local, and is able to store patterns with a finite overlap with the input patterns without ever reaching a spin-glass phase where all memories are lost.

• OSTI ID: 21560287
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 5 Vol. 83; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATTRACTORS
LEARNING
NEURAL NETWORKS
SPIN GLASS STATE