Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

翻译：循环脉冲神经网络（RSNN）已成为一种计算高效且受大脑启发的学习模型。设计具有更少神经元和突触的稀疏RSNN有助于降低其计算复杂度。传统上，稀疏SNN通过先针对目标任务训练密集且复杂的SNN，再在保持任务性能的同时修剪低活性神经元（基于活性的修剪）获得。与此相反，本文提出了一种任务无关的方法，通过修剪大型随机初始化模型来设计稀疏RSNN。我们引入了一种新颖的Lyapunov噪声修剪（LNP）算法，该算法使用图稀疏化方法，并利用Lyapunov指数从随机初始化的RSNN中设计稳定的稀疏RSNN。我们证明LNP能够利用神经元时间尺度的多样性来设计稀疏异质性RSNN（HRSNN）。进一步，我们表明同一稀疏HRSNN模型可针对不同任务（如图像分类和时间预测）进行训练。实验结果显示，尽管是任务无关的，但与传统的基于活性修剪的密集训练模型相比，LNP提高了RSNN的计算效率（更少的神经元和突触）和预测性能。