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：深度前馈和递归型基于发放率的人工神经网络已成为大脑的有效功能模型，但忽略了诸如脉冲发放和戴尔定律等明显的生物学细节。本文论证这些细节对于理解真实神经回路如何运作至关重要。为此，我们提出了一种新的低秩兴奋-抑制脉冲神经网络中的脉冲计算框架。通过考虑秩为1连接性的神经元群体，我们将每个神经元的脉冲发放阈值视为低维输入-输出空间中的边界。我们进一步揭示了抑制性神经元群体的联合阈值在该空间中形成稳定边界，而兴奋性神经元群体的联合阈值则形成不稳定边界。结合这两种边界可得到秩为2的兴奋-抑制（EI）网络，其抑制稳定化动力学位于两边界交汇处。此类网络的计算可理解为两个凸函数的差值，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若干特性，包括噪声抑制与放大、非规则放电活动及突触平衡，并阐明了在边界软化的极限条件下它们与发放率网络动力学的关联。最后，尽管本文研究聚焦于小型网络（5-50个神经元），我们探讨了扩展至更大规模网络的潜在途径。总体而言，本研究提出了脉冲网络的新视角，可为理解生物脉冲计算的机械论基础提供起点。