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Systematic Relational Reasoning With Epistemic Graph Neural Networks

Irtaza Khalid, Steven Schockaert

TL;DR

This work tackles systematic relational reasoning by showing that standard GNNs struggle to generalize to longer inference chains. The authors propose Epistemic GNN (EpiGNN), which treats node embeddings as epistemic states and uses forward/backward path-based reasoning aligned with a differentiable form of directional algebraic closure to handle multi-path disjunctive rules. They introduce RCC-8 and Interval Algebra benchmarks that require aggregating information across multiple paths, where neuro-symbolic methods falter but EpiGNN succeeds, while also performing competitively on inductive knowledge graph completion. The results demonstrate that EpiGNN achieves state-of-the-art or competitive performance on diverse reasoning tasks with a scalable, parameter-efficient architecture, and code is released for reproducibility.

Abstract

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Systematic Relational Reasoning With Epistemic Graph Neural Networks

TL;DR

This work tackles systematic relational reasoning by showing that standard GNNs struggle to generalize to longer inference chains. The authors propose Epistemic GNN (EpiGNN), which treats node embeddings as epistemic states and uses forward/backward path-based reasoning aligned with a differentiable form of directional algebraic closure to handle multi-path disjunctive rules. They introduce RCC-8 and Interval Algebra benchmarks that require aggregating information across multiple paths, where neuro-symbolic methods falter but EpiGNN succeeds, while also performing competitively on inductive knowledge graph completion. The results demonstrate that EpiGNN achieves state-of-the-art or competitive performance on diverse reasoning tasks with a scalable, parameter-efficient architecture, and code is released for reproducibility.

Abstract

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.
Paper Structure (52 sections, 6 theorems, 35 equations, 18 figures, 14 tables)

This paper contains 52 sections, 6 theorems, 35 equations, 18 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Learning to reason in relational domains
  3. Learning to reason about simple path rules
  4. Learning to reason about disjunctive rules
  5. An Epistemic GNN for systematic reasoning
  6. Message passing
  7. Pooling
  8. Training
  9. Facets
  10. Expressivity
  11. Forward-backward model
  12. Experiments
  13. Main results
  14. Ablations
  15. Parameter and time complexity
  16. ...and 37 more sections

Key Result

Proposition 1

We have that $\mathcal{K}\cup\mathcal{F}\models r(a,b)$ holds iff there exists a relational path $r_1;\ldots;r_k$ connecting $a$ and $b$ in the graph $G_{\mathcal{F}}$ such that $r$ can be derived from $r_1;\ldots;r_k$.

Figures (18)

  • Figure 1: Left: A (single) relational path reasoning problem over family relations from CLUTRR clutrr, where the path $P_1$ allows us to infer the correct relation. Right: A multi-path reasoning problem over RCC-8 relations where each path provides partial (disjunctive) information and the target label is obtained by combining information from paths $P_1$, $P_2$ and $P_3$.
  • Figure 2: RCC-8 relations.
  • Figure 3: Overview of the EpiGNN. Step 1: Independently learn the forward and backward entity embeddings through epistemic message passing. Step 2: Compose the entity embeddings on a path between the head (blue) and target (red) entity from the forward and backward model. Each composition predicts the target relation. Step 3: Aggregate the evidence provided by each prediction.
  • Figure 4: RCC-8 and Interval Algebra benchmark results (accuracy). R5 and CTP results for 5+ hops were set to zero since the model took longer than 30 minutes for inference. Models are trained on graphs with $b\in\{1,2,3\}$ paths of length $k\in\{2,3,4\}$. The best model for all cases is EpiGNN-$\texttt{min}$.
  • Figure 5: Parameter complexity across the relation prediction benchmarks.
  • ...and 13 more figures

Theorems & Definitions (12)

  • Proposition 1
  • Proposition 2: informal
  • Example 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • ...and 2 more