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Statistical Mechanics of Neural Networks

Nowadays, the phrase neural network is most often understood as a neural network with a feed-forward connection. However, at the dawn of neural networks, in the eighties, there was no certainty that such networks would be the most common, so a lot of research was carried out, for example, for cyclic neural networks.

In a talk based on the article "Statistical Mechanics Of Neural Networks" by Haim Sompolinsky of the Racah Institute of Physics of the Hebrew University of Jerusalem, published in Physics Today in 1988 (Sompolinsky H. Statistical mechanics of neural networks //Physics Today. – 1988. - V. 41. - No. 21. - P. 70-80.), the statistical regularities of such cyclic networks will be considered.

In the first part of the report, we will talk about how neural networks were understood in those days, what were their characteristics, and what was meant by the memory of neurons. There are no significant changes in modern research, but it is still interesting to look at the ideas of scientists 35 years ago and compare their approach to understanding neural networks with the modern approach.

In the second part of the report, we will delve into specific types of cyclic neural networks, called the Hopfield and Wilshaw models, and also talk about asymmetric synapses (there can be bidirectional connections between neurons - symmetrical and asymmetric)

In the end, we will discuss possible optimizations for such networks, and also talk about statistical patterns in them. And also take a look from the height of modernity at the challenges that the authors of the article put in the conclusion, for example: "It is also not clear to which level of organization in the nervous system these models apply".

Speaker: Filatov Anton Yurievich, assistant of the department MOEM SPbGETU "LETI"

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