FNES: Formulating Natural World Rules via Equiangular Spirals to Strengthen Temporal Knowledge Representation

Existing temporal knowledge graph completion research often extracts features from isolated aspects of temporal facts, which hinders modeling of multi-faceted semantic structures under complex temporal dynamics. This work begins with dynamic characteristics and behavior patterns of entities under independent perturbations of relations or time, and reveals following scenarios: 1)The sensitivity of relations to temporal changes:Different relations between entities show distinct temporal sensitivities as time evolves. 2)Latent perturbations between relations:Different relations mutually perturb and interact, revealing latent internal associations. 3)Snail shell-like time growth effect:Timestamps can be modeled as outward growth of a spiral shell, where each spiral marks a trace of progress, reflecting cumulative and progressive nature of time. To address this, we design a novel model, FNES, inspired by natural structure of snail shells, which maps facts onto corresponding equiangular spirals. Specifically, FNES treats each entity as initial radial distance, maps each relation to a unique rotation angle, and uses each timestamp as a constant controlling rate of radial expansion. As relations gradually extend and timestamps expand outward, spiral structure progressively takes shape. To prevent intersections between spiral trajectories constructed by different entities, FNES learns modulus distribution differences between head and tail entities along$z$-axis. In this way, we provide a compact and coherent encoding structure for facts while simulating real-world rules to the greatest extent possible. Empirically, FNES significantly outperforms SOTA models on six public benchmarks as well as industrial mining datasets.