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.

该论文介绍了一种使用 RTD（Representation Topology Divergence）比较 Recurrent SNN 模型之间分布式表示差异的新方法，探究了使用 STDP 训练的 RSNN 的学习能力以及异质性在突触动力学学习中的作用。

复发射神经网络的异质学习动力学的拓扑表示

Topological Representations of Heterogeneous Learning Dynamics of  Recurrent Spiking Neural Networks

Comparison of data representations is a complex multi-aspect problem that has
not enjoyed a complete solution yet. We propose a method for comparing two data
representations. We introduce the Representation Topology Divergence (RTD),
measuring the dissimilarity in multi-scale topology between two point clouds of
equal size with a one-to-one correspondence between points. The data point
clouds are allowed to lie in different ambient spaces. The RTD is one of the
few TDA-based practical methods applicable to real machine learning datasets.
Experiments show that the proposed RTD agrees with the intuitive assessment of
data representation similarity and is sensitive to its topological structure.
We apply RTD to gain insights on neural networks representations in computer
vision and NLP domains for various problems: training dynamics analysis, data
distribution shift, transfer learning, ensemble learning, disentanglement
assessment.

提出了基于 Representation Topology Divergence (RTD) 的数据表示比较方法，该方法是 few TDA-based practical methods 之一，可以应用于真实的机器学习数据集，用于对计算机视觉和 NLP 领域中的神经网络表示进行分析。