Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions, and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

翻译：深度前馈和递归速率神经网络已成为大脑的功能模型，但它们忽略了诸如脉冲和戴尔定律等明显的生物学细节。本文认为这些细节对于理解真实神经回路如何运作至关重要。为此，我们提出了一个基于脉冲计算的新框架，适用于低秩兴奋-抑制脉冲神经网络。通过考虑秩为1的种群连接，我们将每个神经元的脉冲阈值视为低维输入-输出空间中的边界。我们进而展示了抑制性神经元种群的联合阈值在此空间中形成稳定边界，而兴奋性神经元种群的联合阈值则形成不稳定边界。将两种边界结合可得到一个秩为2的兴奋-抑制（EI）网络，该网络在两个边界的交汇处具有抑制稳定的动力学特性。所得网络的计算可理解为两个凸函数的差，因此能够逼近任意非线性输入-输出映射。我们展示了这些网络的多种特性，包括噪声抑制与放大、不规则活动和突触平衡，以及它们在边界变软极限下如何与速率网络动力学相关联。最后，尽管我们的研究聚焦于小型网络（5-50个神经元），但我们讨论了扩展至更大规模网络的潜在途径。总体而言，本研究为脉冲网络提出了一个全新视角，或可作为理解生物脉冲计算机制机理的起点。