Status-Relational Entropy-AI: A Differentiable Graph Learning Model Based on Topological Dynamics

Graph neural networks (GNNs) based on message-passing mechanisms suffer from well-known over-smoothing: as network depth increases, node representations converge toward identical vectors, degrading prediction performance. In addition, existing temporal GNNs rely on graph snapshots and hand-crafted time-embeddings, lacking native constraints for topological invariants when nodes and edges are continuously added in open-world incremental graphs. This work presents SRE-AI, a differentiable graph learning model built upon Status-Relational Entropy (SRE) topological-dynamics operator suite (Op1-Op10). SRE-AI realizes two critical mechanisms: (1) Dirichlet-energy positive-definite constraint to suppress over-smoothing without architectural modifications; (2) dual-order Betti-number synchronous stitching operator (Op9), which can enforce as hard manifold projection inside forward computation, instead of only soft loss-term regularization. We implement the full SRE operator suite in Rust with analytic adjoint-mode autodifferentiation, wrapped via PyO3 for PyTorch-based training. Experiments are conducted on static molecular dataset OGB-Mol-HIV and dynamic incremental transaction dataset Elliptic. Compared with classical message-passing GNNs (GCN, GAT, GIN) and temporal baselines (TGN, GraphSAGE), SRE-AI maintains competitive or better predictive performance. In particular, under increasing model depth, SRE-AI preserves high Dirichlet energy and avoids severe performance degradation. Long-term rolling incremental experiments further demonstrate that soft-constraint regularization cannot eliminate topological drift, while the hard-constraint Op9 projection stably locks under continuous node expansion.