Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these two forms of signaling? We develop a unified mean-field theory for large random networks to show that first- and second-order statistics in rate and binary networks are in fact identical if rate neurons receive the right amount of noise. Their response to presented stimuli, however, can be radically different. We quantify these differences by studying how nearby state trajectories evolve over time, asking to what extent the dynamics is chaotic. Chaos in the two models is found to be qualitatively different. In binary networks, we find a network-size-dependent transition to chaos and a chaotic submanifold whose dimensionality expands stereotypically with time, while rate networks with matched statistics are nonchaotic. Dimensionality expansion in chaotic binary networks aids classification in reservoir computing and optimal performance is reached within about a single activation per neuron; a fast mechanism for computation that we demonstrate also in spiking networks. A generalization of this mechanism extends to rate networks in their respective chaotic regimes.

中文翻译：

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循环网络的瞬态混沌维数扩展

大脑中的神经元通过尖峰进行交流，尖峰是时间和价值上的离散事件。功能网络模型通常采用由模拟信号连续耦合的速率单位。这两种信号形式是否暗示了质的差异？我们为大型随机网络开发了统一的平均场理论，以表明如果速率神经元接收到适量的噪声，速率和二元网络中的一阶和二阶统计数据实际上是相同的。然而，他们对呈现的刺激的反应可能完全不同。我们通过研究附近的状态轨迹如何随时间演变来量化这些差异，询问动态在多大程度上是混乱的。发现两个模型中的混沌在性质上是不同的。在二元网络中，我们发现了一个与网络大小相关的向混沌的过渡和一个混沌子流形，其维度随时间定型地扩展，而具有匹配统计数据的速率网络是非混沌的。混沌二元网络中的维数扩展有助于储层计算中的分类，并且在每个神经元大约一次激活内达到最佳性能；我们也在尖峰网络中演示的一种快速计算机制。这种机制的推广扩展到在各自的混沌机制中对网络进行评级。我们也在尖峰网络中演示的一种快速计算机制。这种机制的推广扩展到在各自的混沌机制中对网络进行评级。我们也在尖峰网络中演示的一种快速计算机制。这种机制的推广扩展到在各自的混沌机制中对网络进行评级。