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Optimizing One-Shot Learning with Binary Synapses

sandro.romani{at}gmail.com Human Physiology, Università di Roma La Sapienza, Rome 00185, Italy

Daniel J. Amit

amit{at}marx.uchicago.edu INFM, Università di Roma, Rome 00185, Italy, and RacahInstitute of Physics, Hebrew University, Jerusalem 91904, Israel

Yali Amit

amit{at}marx.uchicago.edu Departments of Statistics and Computer Science, Chicago, IL 60637 U.S.A.

A network of excitatory synapses trained with a conservative version of Hebbian learning is used as a model for recognizing the familiarity of thousands of once-seen stimuli from those never seen before. Such networks were initially proposed for modeling memory retrieval (selective delay activity). We show that the same framework allows the incorporation of both familiarity recognition and memory retrieval, and estimate the network's capacity. In the case of binary neurons, we extend the analysis of Amit and Fusi (1994) to obtain capacity limits based on computations of signal-to-noise ratio of the field difference between selective and non-selective neurons of learned signals. We show that with fast learning (potentiation probability approximately 1), the most recently learned patterns can be retrieved in working memory (selective delay activity). A much higher number of once-seen learned patterns elicit a realistic familiarity signal in the presence of an external field. With potentiation probability much less than 1 (slow learning), memory retrieval disappears, whereas familiarity recognition capacity is maintained at a similarly high level. This analysis is corroborated in simulations. For analog neurons, where such analysis is more difficult, we simplify the capacity analysis by studying the excess number of potentiated synapses above the steady-state distribution. In this framework, we derive the optimal constraint between potentiation and depression probabilities that maximizes the capacity.