期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2015
卷号：112
期号：37
页码：11508-11513
DOI：10.1073/pnas.1514188112
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：SignificanceThe activity of a brain--or even a small region of a brain devoted to a particular task--cannot be just the summed activity of many independent neurons. Here we use methods from statistical physics to describe the collective activity in the retina as it responds to complex inputs such as those encountered in the natural environment. We find that the distribution of messages that the retina sends to the brain is very special, mathematically equivalent to the behavior of a material near a critical point in its phase diagram. The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.
关键词：entropy ; information ; neural networks ; Monte Carlo ; correlation
