真实神经元网络的自旋玻璃模型
Spin glass models for a network of real neurons
摘要：
具有成对相互作用的伊辛模型是结构最少或熵最大的概率分布，它精确地再现了测量到的自旋之间的成对相关性。在这里，我们使用这种等价性来构建伊辛模型，该模型描述了蝾螈视网膜中40个神经元对自然电影的响应的相关尖峰活动。我们发现，神经元之间的成对相互作用占观察到的高阶相关性，并且对于10个或更多神经元的组，成对相互作用不再被视为独立系统中的小扰动。然后，我们构建网络集成，概括在实验中观察到的网络实例，并研究其热力学行为和编码能力。基于这种结构，我们还可以创建120个神经元的合成网络，并发现随着规模的增加，网络的运行更接近临界点，并开始表现出让人想起自旋玻璃的集体行为。我们仔细研究了两个这样的行为，可能是相关的神经代码：调整网络的临界点，以最大限度地提高能力，编码不同的刺激，并使用亚稳态的伊辛哈密顿神经代码字。
英文摘要：
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the salamander retina responding to natural movies. We show that pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system. We then construct network ensembles that generalize the network instances observed in the experiment, and study their thermodynamic behavior and coding capacity. Based on this construction, we can also create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses. We examine closely two such behaviors that could be relevant for neural code: tuning of the network to the critical point to maximize the ability to encode diverse stimuli, and using the metastable states of the Ising Hamiltonian as neural code words.
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