Multi-scale signal modulation for variational graph autoencoders

Abstract

Variational graph autoencoder (VGAE) has emerged as a prominent framework for graph representation learning, owing to its probabilistic modeling flexibility and expressive power. Most existing VGAE-based methods assume that the posterior distribution of node embeddings follows a Gaussian distribution and rely on graph convolutional networks with low-pass filtering properties to infer the posterior mean and variance. However, our empirical findings reveal that the variance exhibits non-stationary spectral characteristics, indicating a spectral mismatch between the variance signal and the low-pass nature of conventional inference mechanisms. Further analysis reveals a spectral asymmetry between the posterior mean and variance, as they exhibit distinct signal allocations within the node embeddings. Motivated by these insights, we propose MS-VGAE, a novel variational graph autoencoder with multi-scale signal modulation. Specifically, MS-VGAE leverages a Gabor-based wavelet network to perform fine-grained spectral convolution and signal modulation of the posterior variance across multiple frequency scales. Additionally, a compact optimization objective is derived to enable homophily-aware modulation of frequency-band contributions in the variance. To reduce the computational overhead, we develop MS-VGAE_cheby, which replaces the spectral filtering operation in MS-VGAE with a Chebyshev polynomial approximation. Comprehensive experiments results demonstrate that MS-VGAE achieves satisfactory performance on both node clustering and link prediction tasks. Moreover, MS-VGAE_cheby offers an efficient alternative to MS-VGAE, while maintaining comparable performance on large graphs. The code is available at https://github.com/GDM-SCNU/MS-VGAE.