LiFTER: A Grounded Neuro-Symbolic Microscope for Continuous-Time Dynamic Graph Forecasting

Can a trace explaining model execution also compute the changes needed for a specified alternative prediction? We propose trace-guided intervention search, which uses executable reasoning traces as an intermediate representation for intervention synthesis. A Specified-Foil Counterfactual edits past events so that a frozen temporal predictor selects a designated foil. Our method constructs facts and replacement values from completed original and foil executions and recovered unmet conditions. Proposal generation constructs edits and selects candidates within a fixed cap; exact replay verifies foil top-1 outcomes among retained edits and compositions. Implemented in LiFTER for continuous-time dynamic graphs (CTDGs) and TLogic for temporal knowledge graphs (TKGs), the method improves success over coordinate-based proposal generation by 13.7-34.7 percentage points on four CTDG datasets and 60.0-83.3 points on two TKG datasets under matched downstream search and a proposal cap of 32. Separate shared-candidate comparisons retain 85.7-93.6% of black-box greedy's CTDG success rate with 75.0-80.0% fewer predictor evaluations. A Pulse case study confirms simulator-level survival for five of six interventions. Executable traces thus provide both explanatory evidence and a reusable computational representation for constructing and testing specified alternatives.

Temporal link prediction (TLP) is typically evaluated by predictive performance on unseen edges, but this criterion can conflate predictive accuracy with recovery of the underlying causal mechanism. In stochastic models, Fisher information governs the Cramér--Rao (CR) bound on parameter estimation error: higher Fisher information permits more accurate parameter recovery. We show that, under comonotonicity conditions between Fisher information and entropy, binary logistic models exhibit an estimation--prediction tradeoff: regimes with higher Fisher information, and hence smaller CR bounds, also have higher irreducible predictive entropy. To study this tradeoff in TLP, we introduce a probabilistic causal generator for temporal graphs with transient edges and known ground-truth causal structure, and validate the phenomenon empirically.

Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.