Spiking neural networks (SNNs) are a viable alternative to conventional artificial neural networks when resource efficiency and computational complexity are of importance. A major advantage of SNNs is their binary information transfer through spike trains which eliminates multiplication operations. The training of SNNs has, however, been a challenge, since neuron models are non-differentiable and traditional gradient-based backpropagation algorithms cannot be applied directly. Furthermore, spike-timing-dependent plasticity (STDP), albeit being a spike-based learning rule, updates weights locally and does not optimize for the output error of the network. We present desire backpropagation, a method to derive the desired spike activity of all neurons, including the hidden ones, from the output error. By incorporating this desire value into the local STDP weight update, we can efficiently capture the neuron dynamics while minimizing the global error and attaining a high classification accuracy. That makes desire backpropagation a spike-based supervised learning rule. We trained three-layer networks to classify MNIST and Fashion-MNIST images and reached an accuracy of 98.41% and 87.56%, respectively. In addition, by eliminating a multiplication during the backward pass, we reduce computational complexity and balance arithmetic resources between forward and backward pass, making desire backpropagation a candidate for training on low-resource devices.

翻译：脉冲神经网络（SNN）在资源效率和计算复杂度至关重要的情况下，是传统人工神经网络的可行替代方案。SNN的主要优势在于其通过脉冲序列进行二进制信息传递，从而消除了乘法运算。然而，由于神经元模型不可微且传统的基于梯度的反向传播算法无法直接应用，SNN的训练一直是一个挑战。此外，脉冲时序依赖可塑性（STDP）虽然是一种基于脉冲的学习规则，但仅局部更新权重，并不针对网络的输出误差进行优化。我们提出欲望反向传播方法，该方法从输出误差中导出所有神经元（包括隐藏层神经元）的期望脉冲活动。通过将该欲望值纳入局部STDP权重更新中，我们能够高效捕捉神经元动态，同时最小化全局误差并获得高分类精度。这使得欲望反向传播成为一种基于脉冲的监督学习规则。我们训练了三层网络来分类MNIST和Fashion-MNIST图像，分别达到了98.41%和87.56%的准确率。此外，通过消除反向传播过程中的乘法运算，我们降低了计算复杂度并平衡了前向和反向传播之间的算术资源，使欲望反向传播成为低资源设备上训练的理想候选方案。