Bridging the Gap Between Plausibility and Admissibility: Constraint-Aware Flow Maps for Dynamic Graph Systems

2026-07-23

AI Summary

This work addresses the tendency of generative models to produce statistically plausible yet structurally infeasible dynamic graph trajectories. To explicitly enforce structural admissibility, we propose integrating a conditional diffusion model with an external symbolic constraint layer, employing three mechanisms: hard filtering, soft weighting, and projection-based repair. We formally distinguish statistical plausibility from structural admissibility as two independent reliability attributes and demonstrate that symbolic constraints become especially critical in high-complexity graph systems. Experimental results show that in compact graphs, the proportion of invalid trajectories drops to as low as 0.002996; under moderate complexity, hard filtering retains 84.4% of valid samples while entirely eliminating infeasible outputs, confirming that constraint violations are the primary source of structural unacceptability.

Abstract

Generative models can support decision-making under uncertainty by producing ensembles of plausible future system trajectories, but statistical plausibility does not ensure structural feasibility. This study investigates whether post-sampling symbolic constraints can improve the reliability of generative trajectory modeling in dynamic graph-structured systems. A conditional diffusion model generates future graph-state trajectories from partial observations, while an external symbolic layer applies hard filtering, soft weighting, or projection-based repair. The framework is evaluated on two controlled synthetic regimes: a compact graph and a medium-complexity dependency graph, using metrics for structural validity, sample efficiency, diversity, robustness, and calibration. In the compact regime, the model produces an invalid probability mass of 0.002996, indicating an almost entirely admissible trajectory manifold. Under the same architecture and training protocol, invalid mass increases to 0.155929 in the medium-complexity regime. Hard filtering removes all invalid retained trajectories while preserving 84.4% of generated samples, whereas soft weighting preserves effective sample size but yields only limited validity gains. Family-level analysis shows that dependency constraints account for nearly all observed inadmissibility. These results indicate that statistical plausibility and structural admissibility are distinct reliability properties and that symbolic constraint handling becomes more valuable as graph-structural complexity increases.

Problem

• plausibility
• admissibility
• dynamic graph systems
• structural constraints
• generative trajectory modeling

Innovation

• constraint-aware generative modeling
• dynamic graph systems
• symbolic constraint integration
• diffusion models
• structural admissibility