Learning Time-Varying Relational Constraints on Dynamic Heterogeneous Graphs

I study when changing rules that link related nodes on a typed, time-varying graph can be recovered from the observations, and which kind of model is needed in each case. I call this change *relational-semantics drift*: two nodes should still satisfy $x_v\approx R_{r,t}^{\star }{x}_u$, but the map $R_{r,t}^{\star }$ can move even when the graph shape and node features look similar. What can be recovered depends on what the data still contains. If each node is reduced to a mixed average over all neighbor types, that average no longer depends on the typed maps, so the maps cannot be recovered. The raw typed pairs $(x_u,x_v)$ do keep the map: orthogonal Procrustes recovers it when the map stays in $\text{SO}(d)$, and least squares recovers it when the map is in $\text{GL}(d)$. A Cayley sheaf with a slow path and a fast path improves anomaly scores when the planted rule changes smoothly, beating TGN, DualPath, and aggregated Procrustes and matching EvolveGCN; it tracks coboundary energy, not a typed ${\hat{R}}_r$. Averaging nodes first does *not* recover unlabeled jumps ($0.595\pm 0.071$ vs. DualPath $0.590\pm 0.062$). When the pairs themselves are observed, unlabeled trimmed least squares in $\text{GL}(d)$ recovers the post-jump residual (five-seed AUC $1.000$); orthogonal Procrustes fails if the jump leaves $\text{SO}(d)$.