Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is quite expensive. Furthermore, after training, all information related to the computational task is hidden into the weight matrix, prohibiting us from a transparent understanding of circuit mechanisms. Therefore, in this work, we address these challenges by proposing a spiking mode-based training protocol, where the recurrent weight matrix is explained as a Hopfield-like multiplication of three matrices: input, output modes and a score matrix. The first advantage is that the weight is interpreted by input and output modes and their associated scores characterizing the importance of each decomposition term. The number of modes is thus adjustable, allowing more degrees of freedom for modeling the experimental data. This significantly reduces the training cost because of significantly reduced space complexity for learning. Training spiking networks is thus carried out in the mode-score space. The second advantage is that one can project the high dimensional neural activity (filtered spike train) in the state space onto the mode space which is typically of a low dimension, e.g., a few modes are sufficient to capture the shape of the underlying neural manifolds. We successfully apply our framework in two computational tasks -- digit classification and selective sensory integration tasks. Our method accelerate the training of spiking neural networks by a Hopfield-like decomposition, and moreover this training leads to low-dimensional attractor structures of high-dimensional neural dynamics.

翻译：脉冲神经网络在类脑神经形态计算及神经回路工作机制研究中扮演重要重要角色。训练大规模脉冲神经网络的一个缺陷在于更新所有权重的代价十分高昂。此外，训练完成后，所有与计算任务相关的信息均隐藏于权重矩阵中，阻碍了我们对回路机制形成透明化的理解。因此，在本工作中，我们通过提出一种基于脉冲模式的训练协议来解决这些挑战，其中循环权重矩阵被解释为三个矩阵的类Hopfield乘法：输入模式、输出模式及评分矩阵。其首要优势在于，权重可通过输入/输出模式及其关联评分进行解释，这些评分表征了每个分解项的重要性。模式数量因而可调，为实验数据建模提供了更多自由度。由于学习所需的空间复杂度显著降低，这大幅减少了训练成本。脉冲网络的训练由此在模式-评分空间中进行。第二个优势在于，可将高维神经活动（滤波后的脉冲序列）从状态空间投影到通常是低维的模式空间，例如仅需少量模式即可捕捉底层神经流形的形态。我们成功地将该框架应用于两项计算任务——数字分类与选择性感觉整合任务。我们的方法通过类Hopfield分解加速了脉冲神经网络的训练，并且这种训练能引导高维神经动力学形成低维吸引子结构。