Accumulated detailed knowledge about the neuronal activities in human brains has brought more attention to bio-inspired spiking neural networks (SNNs). In contrast to non-spiking deep neural networks (DNNs), SNNs can encode and transmit spatiotemporal information more efficiently by exploiting biologically realistic and low-power event-driven neuromorphic architectures. However, the supervised learning of SNNs still remains a challenge because the spike-timing-dependent plasticity (STDP) of connected spiking neurons is difficult to implement and interpret in existing backpropagation learning schemes. This paper proposes a fractional-order spike-timing-dependent gradient descent (FO-STDGD) learning model by considering a derived nonlinear activation function that describes the relationship between the quasi-instantaneous firing rate and the temporal membrane potentials of nonleaky integrate-and-fire neurons. The training strategy can be generalized to any fractional orders between 0 and 2 since the FO-STDGD incorporates the fractional gradient descent method into the calculation of spike-timing-dependent loss gradients. The proposed FO-STDGD model is tested on the MNIST and DVS128 Gesture datasets and its accuracy under different network structure and fractional orders is analyzed. It can be found that the classification accuracy increases as the fractional order increases, and specifically, the case of fractional order 1.9 improves by 155% relative to the case of fractional order 1 (traditional gradient descent). In addition, our scheme demonstrates the state-of-the-art computational efficacy for the same SNN structure and training epochs.

翻译：人类大脑神经元活动知识的不断积累，使得受生物启发的脉冲神经网络（SNNs）受到更多关注。与非脉冲的深度神经网络（DNNs）相比，SNNs能够通过利用生物真实性高且低功耗的事件驱动神经形态架构，更高效地编码和传递时空信息。然而，SNNs的监督学习仍然是一个挑战，因为连接脉冲神经元的脉冲时序依赖可塑性（STDP）在现有的反向传播学习方案中难以实现和解释。本文通过考虑一个描述非泄漏积分发放神经元的准瞬时发放率与瞬时膜电位之间关系的推导非线性激活函数，提出了一种分数阶脉冲时序依赖梯度下降（FO-STDGD）学习模型。该训练策略可推广至0到2之间的任意分数阶，因为FO-STDGD将分数阶梯度下降方法融入了脉冲时序依赖损失梯度的计算中。所提出的FO-STDGD模型在MNIST和DVS128 Gesture数据集上进行了测试，并分析了其在不同网络结构和分数阶下的准确率。可以发现，分类准确率随分数阶的增加而提高，特别是分数阶为1.9的情况相对于分数阶为1（传统梯度下降）的情况提升了155%。此外，我们的方案在相同的SNN结构和训练轮次下展示了最先进的计算效率。