Tkačik Gašper, Mora Thierry, Marre Olivier, Amodei Dario, Palmer Stephanie E, Berry Michael J, Bialek William
Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria;
Laboratoire de Physique Statistique, CNRS, Université Pierre et Marie Curie (UPMC) and l'École Normale Supérieure, 75231 Paris Cedex 05, France;
Proc Natl Acad Sci U S A. 2015 Sep 15;112(37):11508-13. doi: 10.1073/pnas.1514188112. Epub 2015 Sep 1.
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.
神经网络的活动由单个神经元的放电和静息模式定义。由于放电（相对）稀疏，随着放电数量增加，活动模式出现的可能性降低，但随着放电数量增多，可能的模式数量会增加。这种概率与数量之间的权衡在数学上等同于统计物理学中熵与能量之间的关系。我们通过对该网络对自然主义电影的响应实验进行直接分析和基于模型的分析相结合，构建了脊椎动物视网膜一小片区域中多达N = 160个神经元群体的这种关系。我们看到了热力学极限的迹象，即随着N增加，每个神经元的熵接近每个神经元能量的平滑函数。该函数的形式对应于活动分布在一种不寻常的临界点附近保持平衡。我们建议进一步进行临界性测试，并简要讨论其功能意义。
