Quotient-Residual Temporal Memory for Scalable Continuous-Time Graph Learning

Continuous-time temporal graph models maintain evolving node states and repeatedly propagate information as timestamped interactions arrive. Their accuracy comes with a persistent cost: the state and propagation domain grow with the original graph. Graph coarsening can reduce this domain, but prior coarse-to-fine pipelines recover accuracy through full-graph fine-tuning and memory reconstruction, which reintroduces the resource that coarsening was intended to remove. We introduce the Quotient-Residual Temporal Network (QRTN), a fine-tuning-free framework that preserves every timestamped event while separating shared quotient dynamics from a small identity-preserving residual. QRTN provides three operating points. QRTN-M processes original-node events throughout training while storing high-dimensional state only on supernodes. QRTN-X trains shared temporal operators on an event-preserving quotient and transfers parameters, but no runtime state, to a fresh original graph. QRTN-X-Gated uses the same quotient training but initialises original-node runtime state through a fixed, attenuated lift of the learned quotient state, without replay or original-graph gradient updates. These modes expose an auditable choice among persistent memory compression, strict parameter-only transfer, and state-initialised transfer. We provide a causal formulation, exact state accounting, and time-complexity bounds that distinguish node compression from event reduction. The accompanying evaluation protocol tests accuracy, inductive prediction, oversmoothing, cold-start behaviour, and end-to-end resource use across coarsening ratios.