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：深度前馈和循环速率神经网络已成为脑功能模型的有效工具，但忽略了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的工作机制至关重要。为此，我们提出了一种基于低秩兴奋-抑制脉冲网络进行脉冲计算的新框架。通过考虑秩为1的群体连接，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。随后证明，抑制性神经元群体的组合阈值在该空间中形成稳定边界，而兴奋性神经元群体的组合阈值则形成不稳定边界。将这两个边界结合可得到一个秩为2的兴奋-抑制（EI）网络，其在边界交汇处呈现抑制稳定化动力学。所得网络的计算可理解为两个凸函数的差值，从而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、不规则活动及突触平衡，并阐明了当边界趋于软化时它们与速率网络动力学之间的关联。最后，虽然我们的工作聚焦于小型网络（5-50个神经元），但探讨了扩展至更大规模网络的潜在路径。总体而言，本研究为脉冲网络提供了新视角，有望成为理解生物脉冲计算机制的起点。