Artificial neural networks are highly successfully trained with backpropagation. For spiking neural networks, however, a similar gradient descent scheme seems prohibitive due to the sudden, disruptive (dis-)appearance of spikes. Here, we demonstrate exact gradient descent learning based on spiking dynamics that change only continuously. These are generated by neuron models whose spikes vanish and appear at the end of a trial, where they do not influence other neurons anymore. This also enables gradient-based spike addition and removal. We apply our learning scheme to induce and continuously move spikes to desired times, in single neurons and recurrent networks. Further, it achieves competitive performance in a benchmark task using deep, initially silent networks. Our results show how non-disruptive learning is possible despite discrete spikes.

翻译：人工神经网络通过反向传播成功实现了高效训练。然而，对于脉冲神经网络而言，类似的梯度下降方法似乎难以实现，因为脉冲的突然出现或消失会带来破坏性影响。本文证明，基于仅连续变化的脉冲动力学可以实现精确的梯度下降学习。这种动力学由神经元模型生成，其脉冲在试验结束时消失或出现，且不再影响其他神经元。该方法还支持基于梯度的脉冲添加与删除。我们将该学习方案应用于单神经元和循环网络，以实现脉冲的诱导生成及其连续移动至目标时间点。此外，该方法在深度初始静默网络的基准任务中取得了竞争性表现。我们的结果表明，尽管存在离散脉冲，非破坏性学习仍是可行的。