title: Inference and learning in sparse systems with multiple states.
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.
authors: Human Genetics Foundation, Via Nizza 52, I-10126 Torino, Italy. alfredo.braunstein@polito.it
authors: A
authors: A
authors: Braunstein
authors: A
authors: A
authors: Ramezanpour
authors: R
authors: R
authors: Zecchina
authors: P
authors: P
authors: Zhang
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D010363:Pattern Recognition, Automated