Abstract: The supervised learning method based on gradient descent is to make the neuron can emit desired spike train by minimizing the error between the actual output spike train and the desired spike train using computation of gradient descent. However the error function is constructed dynamically by the actual output spike train and the corresponding desired spike train. That would lead to the number of actual output spike train and the desired spike train being unequal when the algorithm converges. This paper proposes an improved learning algorithm based on gradient descent and it detects the number of spikes in the desired output spike train and the actual output spike train. The algorithm uses a novel error function which is constructed with extra virtual actual spike and virtual desired spike to solve the problem of less or redundant output. Experimental results show that it can effectively prevent the early ending of learning with unequal number of output spike and make the neuron emit the desired spike train precisely.

Key words: spiking neuron, spike train, precise learning, gradient descent, virtual spike

摘要： 基于梯度下降的脉冲神经元有监督学习算法通过计算梯度最小化目标序列和实际输出序列间的误差使得神经元能激发出目标脉冲序列。然而该算法中的误差函数是基于实际输出脉冲序列和相对应的目标输出脉冲序列动态构建而成，导致算法在收敛时可能出现实际输出序列的个数和期望输出个数不相等的情况。针对这一缺陷提出了一种改进的脉冲神经元梯度下降学习算法，算法在学习过程中检测目标序列脉冲个数和实际激发脉冲个数，并引入虚拟实际激发脉冲和期望激发脉冲构建误差函数以分别解决激发个数不足和激发个数多余的问题。实验结果证明该算法能有效地防止学习算法在输出脉冲个数不等的情况下提前结束，使得神经元能够精确地激发出目标脉冲序列。

关键词: 脉冲神经元, 脉冲序列, 精确学习, 梯度下降, 虚拟脉冲