Variational autoencoders (VAEs) have been widely used for node clustering, with existing methods mainly focusing on enhancing the expressiveness of their latent space. Recently, the integration of diffusion models with VAEs has provided new opportunities to achieve this objective. However, the mechanism by which the diffusion model improves performance remains unclear. To bridge this gap, we conduct an empirical analysis from the perspective of graph spectral theory, revealing that the signal modulation induced by diffusion models closely aligns with the low-frequency spectral characteristics of VAEs, which in turn explains their effectiveness. Nevertheless, further experiments highlight that diffusion models exhibit limitations in modulating high-frequency signals, which diverge from the spectral characteristics of VAEs. Moreover, existing diffusion methods fail to enable the latent space to adequately capture and reflect cluster-specific characteristics. To address these challenges, we propose a novel plug-and-play method, FVD, to improve the performance of VAE-based methods in node clustering tasks. Specifically, we incorporate the graph wavelet transform as a secondary signal modulator, enabling independent adjustments of specific frequency bands to better align with the spectral characteristics of VAEs. Additionally, we introduce the Student's t-distribution as a conditional constraint in the reverse process of FVD, deriving a more compact variational lower bound. This enhancement preserves fine-grained node information while focusing on clustering details, effectively mitigating the cluster collapse phenomenon. Comprehensive experimental results demonstrate that integrating FVD with existing methods achieves competitive performance improvements in most cases.

Variational autoencoder performs well in community detection on static networks, but it is difficult to directly extend to continuous dynamic networks. The main reason is that traditional methods mainly rely on adjacency structures to complete the inference and generation processes. However, continuous dynamic networks cannot be described by this structure because the inherent timeliness and causality information of the network would be lost. To address this issue, we propose a novel variational autoencoder, CT-VAE, for community detection in continuous dynamic networks, along with its scalable variant, CT-CAVAE. By conceptualizing node interactions as event streams and adopting the Hawkes process to capture temporal dynamics and causality, and incorporating them into the inference process, CT-VAE can effectively extend the traditional inference approach to continuous dynamic networks. Additionally, in the generation phase, CT-VAE combines pseudo-labeling and compact constraint strategies to facilitate the reconstruction process of non-adjacent structures. For the scalable variant, CT-CAVAE, end-to-end community detection is achieved by cleverly combining Gaussian mixture distribution. Extensive experimental results demonstrate that the proposed CT-VAE and CT-CAVAE achieve more favorable performance compared with the state-of-the-art baselines.

Modeling nonlinear dynamical systems is a challenging task in fields such as speech processing, music generation, and video prediction. This paper introduces a hierarchical framework for Deep State Space Models (DSSMs), categorizing them by their conditional independence properties and Markov assumptions and positioning existing models within this framework, including the Stochastic Recurrent Neural Network (SRNN), Variational Recurrent Neural Network (VRNN), and Recurrent State Space Model (RSSM). We discuss different options for the inference networks and demonstrate how integrating normalizing flows can enhance model flexibility by capturing complex distributions. Our work not only clarifies the relationships among existing models but also paves the way for the development of new, more effective approaches for modeling nonlinear dynamics. In particular, we propose the Autoregressive State Space Model (ArSSM) and evaluate its effectiveness in speech and polyphonic music modeling tasks.

Methods based on variational bayes theorytare widely used to detect community structures in networks. In recent years, many related methods have emerged that provide valuable insights into variational bayes theory. Remarkably, a fundamental assumption remains incomprehensible. Variational bayes-based methods typically employ a posterior distribution that follows a gaussian distribution to approximate the unknown prior distribution. However, the complexity and irregularity of node distributions in real-world networks prompt us to consider what characteristics of network information are suitable for the posterior distribution. Mathematically, inappropriate low- and high-frequency signals in expectation inference and variance inference can intensify the adverse effects of community distortion and ambiguity. To analysis these two phenomena and propose reasonable countermeasures, we conduct an empirical study. It is found that appropriately compressing low-frequency signals during expectation inference and amplifying high-frequency signals during variance inference are effective strategies. Based on these two strategies, this paper proposes a novel variational bayes plug-in, namely VBPG, to boost the performance of existing variational bayes-based community detection methods. Specifically, we modulate the frequency signals during expectation and variance inference to generate a new gaussian distribution. This strategy improves the fitting accuracy between the posterior distribution and the unknown true distribution without altering the modules of existing methods. The comprehensive experimental results validate that methods using VBPG achieve competitive performance improvements in most cases.