TF²-Net: treg-regulated Fourier Transformer for homeostatic community detection in dynamic graphs

Community detection in dynamic graphs often suffers from unstable embeddings and temporal drift when network structures evolve rapidly or irregularly. Existing graph neural and Transformer-based models capture temporal correlations effectively but tend to amplify spectral noise and lose interpretability. Inspired by biological homeostasis and spectral signal regulation, we propose TF²-Net (Treg-Regulated Fourier Transformer Network), a hybrid framework integrating graph Fourier analysis, Transformer attention, and T-regulatory (Treg) feedback control for stabilized community detection. TF²-Net decomposes each graph snapshot into Laplacian eigenmodes to obtain a spectral frequency representation, where the Fourier transformer encoder selectively attends to stable eigenmodes associated with global community patterns. To prevent spectral drift and over-activation, a Treg-inspired inhibitory regulator dynamically adjusts attention weights via negative feedback, ensuring embedding homeostasis across temporal snapshots. The model optimizes a stability-regularized spectral loss, combining modularity, spectral smoothness, and homeostatic equilibrium. Experiments on citation, social, and biological dynamic networks show that TF²-Net achieves superior clustering performance in ARI, NMI, and modularity while maintaining low embedding variance and improved stability index ρ. The model bridges spectral graph learning, Transformer attention, and biological regulation, offering a pathway toward interpretable, self-stabilizing graph intelligence.