Spiking neural networks (SNNs) with event-based computation are promising brain-inspired models for energy-efficient applications on neuromorphic hardware. However, most supervised SNN training methods, such as conversion from artificial neural networks or direct training with surrogate gradients, require complex computation rather than spike-based operations of spiking neurons during training. In this paper, we study spike-based implicit differentiation on the equilibrium state (SPIDE) that extends the recently proposed training method, implicit differentiation on the equilibrium state (IDE), for supervised learning with purely spike-based computation, which demonstrates the potential for energy-efficient training of SNNs. Specifically, we introduce ternary spiking neuron couples and prove that implicit differentiation can be solved by spikes based on this design, so the whole training procedure, including both forward and backward passes, is made as event-driven spike computation, and weights are updated locally with two-stage average firing rates. Then we propose to modify the reset membrane potential to reduce the approximation error of spikes. With these key components, we can train SNNs with flexible structures in a small number of time steps and with firing sparsity during training, and the theoretical estimation of energy costs demonstrates the potential for high efficiency. Meanwhile, experiments show that even with these constraints, our trained models can still achieve competitive results on MNIST, CIFAR-10, CIFAR-100, and CIFAR10-DVS. Our code is available at https://github.com/pkuxmq/SPIDE-FSNN.

翻译：脉冲神经网络（SNN）凭借其基于事件的计算特性，成为在神经形态硬件上实现高能效应用的极具前景的类脑模型。然而，大多数监督式SNN训练方法（如从人工神经网络转换或使用替代梯度直接训练）在训练过程中需要复杂的计算，而非脉冲神经元本身的脉冲运算。本文研究了基于平衡态的脉冲隐式微分方法（SPIDE），该方法将近期提出的基于平衡态的隐式微分训练方法（IDE）扩展到纯脉冲计算驱动的监督学习场景，展示了SNN高能效训练的潜力。具体而言，我们引入了三元脉冲神经元耦合对，并证明基于该设计可通过脉冲实现隐式微分求解，从而使前向和反向传播的完整训练过程均变为事件驱动的脉冲计算，并通过两阶段平均发放率实现局部权重更新。随后，我们提出修改重置膜电位以降低脉冲的近似误差。借助这些关键组件，我们能够以较少时间步和训练期间脉冲稀疏性的方式训练具有灵活结构的SNN，理论能耗估算表明其具备高效率潜力。同时，实验证明即使存在这些约束，我们的训练模型仍能在MNIST、CIFAR-10、CIFAR-100和CIFAR10-DVS数据集上取得具有竞争力的结果。代码已开源在https://github.com/pkuxmq/SPIDE-FSNN。