Spiking Neural Networks (SNNs) have become an essential paradigm in neuroscience and artificial intelligence, providing brain-inspired computation. Recent advances in literature have studied the network representations of deep neural networks. However, there has been little work that studies representations learned by SNNs, especially using unsupervised local learning methods like spike-timing dependent plasticity (STDP). Recent work by \cite{barannikov2021representation} has introduced a novel method to compare topological mappings of learned representations called Representation Topology Divergence (RTD). Though useful, this method is engineered particularly for feedforward deep neural networks and cannot be used for recurrent networks like Recurrent SNNs (RSNNs). This paper introduces a novel methodology to use RTD to measure the difference between distributed representations of RSNN models with different learning methods. We propose a novel reformulation of RSNNs using feedforward autoencoder networks with skip connections to help us compute the RTD for recurrent networks. Thus, we investigate the learning capabilities of RSNN trained using STDP and the role of heterogeneity in the synaptic dynamics in learning such representations. We demonstrate that heterogeneous STDP in RSNNs yield distinct representations than their homogeneous and surrogate gradient-based supervised learning counterparts. Our results provide insights into the potential of heterogeneous SNN models, aiding the development of more efficient and biologically plausible hybrid artificial intelligence systems.

翻译：脉冲神经网络（SNNs）已成为神经科学与人工智能领域的重要范式，能够实现类脑计算。近年文献研究了深度神经网络的网络表征，但针对SNN所学表征的研究仍较匮乏，尤其是采用脉冲时序依赖可塑性（STDP）等无监督局部学习方法时。最近，\cite{barannikov2021representation} 提出了一种用于比较所学表征拓扑映射的新方法——表征拓扑散度（RTD）。尽管该方法有效，但其专为前馈深度神经网络设计，无法直接用于递归脉冲神经网络（RSNN）等递归网络。本文提出一种利用RTD衡量不同学习方法下RSNN模型分布式表征差异的新方法。我们通过带跳跃连接的前馈自编码器网络对RSNN进行重构，从而计算递归网络的RTD。基于此，我们探究了采用STDP训练的RSNN的学习能力，以及突触动力学异质性在表征学习中的关键作用。实验表明，相较于同质化STDP与基于替代梯度的监督学习方法，异质化STDP能使RSNN学习到截然不同的表征。本研究揭示了异质SNN模型的潜力，为构建更高效且符合生物合理性的混合人工智能系统提供了新见解。