Inference and learning in sparse systems with multiple states

A. Braunstein, A. Ramezanpour, R. Zecchina, and P. Zhang
Phys. Rev. E 83, 056114 – Published 19 May 2011

Abstract

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.

    • Received 4 January 2011

    DOI:https://doi.org/10.1103/PhysRevE.83.056114

    ©2011 American Physical Society

    Authors & Affiliations

    A. Braunstein1,2,*, A. Ramezanpour2,†, R. Zecchina2,1,3,‡, and P. Zhang2,§

    • 1Human Genetics Foundation, Via Nizza 52, I-10126 Torino, Italy
    • 2Politecnico di Torino, C.so Duca degli Abruzzi 24, I-10129 Torino, Italy
    • 3Collegio Carlo Alberto, Via Real Collegio 30, I-10024 Moncalieri, Italy

    • *alfredo.braunstein@polito.it
    • abolfazl.ramezanpour@polito.it
    • riccardo.zecchina@polito.it
    • §pan.zhang@polito.it

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    Issue

    Vol. 83, Iss. 5 — May 2011

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