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Temporal Inductive Logic Reasoning over Hypergraphs

Yuan Yang, Siheng Xiong, Ali Payani, James C Kerce, Faramarz Fekri

TL;DR

Temporal Inductive Logic Reasoning (TILR) extends ILP to temporal hypergraphs, enabling learning of interpretable first-order rules over time-interval labeled, higher-order relations. The framework introduces a Multi-start Random B-walk (MRBW) for traversing B-connected hyperedges and integrates Allen's interval algebra with path-consistency to generalize temporal relations, culminating in a differentiable model that scores sampled reasoning paths. Two new benchmarks, YouCook2-HG and nuScenes-HG, demonstrate that TILR outperforms both graph-based baselines and traditional ILP approaches, with improved accuracy and interpretability on tasks like recipe summarization and driving-behavior explanation. The work provides a principled approach to reasoning over complex temporal graphs, with practical impact for structured video instructions, scene understanding, and autonomous systems.

Abstract

Inductive logic reasoning is a fundamental task in graph analysis, which aims to generalize patterns from data. This task has been extensively studied for traditional graph representations, such as knowledge graphs (KGs), using techniques like inductive logic programming (ILP). Existing ILP methods assume learning from KGs with static facts and binary relations. Beyond KGs, graph structures are widely present in other applications such as procedural instructions, scene graphs, and program executions. While ILP is beneficial for these applications, applying it to those graphs is nontrivial: they are more complex than KGs, which usually involve timestamps and n-ary relations, effectively a type of hypergraph with temporal events. In this work, we propose temporal inductive logic reasoning (TILR), an ILP method that reasons on temporal hypergraphs. To enable hypergraph reasoning, we introduce the multi-start random B-walk, a novel graph traversal method for hypergraphs. By combining it with a path-consistency algorithm, TILR learns logic rules by generalizing from both temporal and relational data. To address the lack of hypergraph benchmarks, we create and release two temporal hypergraph datasets: YouCook2-HG and nuScenes-HG. Experiments on these benchmarks demonstrate that TILR achieves superior reasoning capability over various strong baselines.

Temporal Inductive Logic Reasoning over Hypergraphs

TL;DR

Temporal Inductive Logic Reasoning (TILR) extends ILP to temporal hypergraphs, enabling learning of interpretable first-order rules over time-interval labeled, higher-order relations. The framework introduces a Multi-start Random B-walk (MRBW) for traversing B-connected hyperedges and integrates Allen's interval algebra with path-consistency to generalize temporal relations, culminating in a differentiable model that scores sampled reasoning paths. Two new benchmarks, YouCook2-HG and nuScenes-HG, demonstrate that TILR outperforms both graph-based baselines and traditional ILP approaches, with improved accuracy and interpretability on tasks like recipe summarization and driving-behavior explanation. The work provides a principled approach to reasoning over complex temporal graphs, with practical impact for structured video instructions, scene understanding, and autonomous systems.

Abstract

Inductive logic reasoning is a fundamental task in graph analysis, which aims to generalize patterns from data. This task has been extensively studied for traditional graph representations, such as knowledge graphs (KGs), using techniques like inductive logic programming (ILP). Existing ILP methods assume learning from KGs with static facts and binary relations. Beyond KGs, graph structures are widely present in other applications such as procedural instructions, scene graphs, and program executions. While ILP is beneficial for these applications, applying it to those graphs is nontrivial: they are more complex than KGs, which usually involve timestamps and n-ary relations, effectively a type of hypergraph with temporal events. In this work, we propose temporal inductive logic reasoning (TILR), an ILP method that reasons on temporal hypergraphs. To enable hypergraph reasoning, we introduce the multi-start random B-walk, a novel graph traversal method for hypergraphs. By combining it with a path-consistency algorithm, TILR learns logic rules by generalizing from both temporal and relational data. To address the lack of hypergraph benchmarks, we create and release two temporal hypergraph datasets: YouCook2-HG and nuScenes-HG. Experiments on these benchmarks demonstrate that TILR achieves superior reasoning capability over various strong baselines.
Paper Structure (15 sections, 13 equations, 3 figures, 4 tables, 2 algorithms)

This paper contains 15 sections, 13 equations, 3 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Temporal Hypergraphs
  4. Temporal Inductive Logic Reasoning
  5. Random Walk on Temporal Hypergraphs
  6. Temporal Relation Generalization
  7. Differentiable TILR for hypergraph reasoning
  8. Experiment
  9. Recipe summarization
  10. Driving behavior explanation
  11. Conclusion
  12. Acknowledgement
  13. Hypergraphs
  14. Example Hypergraphs
  15. Experiments

Figures (3)

  • Figure 1: Temporal hypergraph representation of video instructions for making spaghetti $\&$ meatballs.
  • Figure 2: Example B-graph and B-paths.
  • Figure 3: Example temporal hypergraphs for recipes Onion rings, Shepherd's Pie, and Tuna Sashimi.

Theorems & Definitions (2)

  • Definition 3.1: Temporal Hypergraph
  • Definition 4.1: Temporal Inductive Logic Reasoning