A Neuro-Symbolic Framework for Answering Graph Pattern Queries in Knowledge Graphs

TL;DR

This work tackles graph pattern query answering over incomplete knowledge graphs, where existing neural approaches are mostly restricted to anchored tree-like queries. It introduces UnRavL, a trainable framework that first unraveled cyclic queries into tree-like forms at a tunable depth $d$ and then evaluates them with a neuro-symbolic processor based on Neural Bellman-Ford Networks to propagate likelihoods along relations. The approach provides formal guarantees (Safety, Conservativeness, Optimality) and supports existential leaves, negation, and disjunction, enabling efficient handling of cyclic and unanchored patterns. Empirical results on FB15k-237, FB15k, and NELL995 show competitive performance for cyclic and unanchored tree-like queries, while preserving strong performance on anchored tree-like queries, highlighting practical impact for scalable, interpretable knowledge graph querying under incompleteness.

Abstract

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high interpretability. These models utilize trained architectures to execute atomic queries and integrate modules that mimic symbolic query operators. However, most neuro-symbolic query processors are constrained to tree-like graph pattern queries. These queries admit a bottom-up execution with constant values or anchors at the leaves and the target variable at the root. While expressive, tree-like queries fail to capture critical properties in knowledge graphs, such as the existence of multiple edges between entities or the presence of triangles. We introduce a framework for answering arbitrary graph pattern queries over incomplete knowledge graphs, encompassing both cyclic queries and tree-like queries with existentially quantified leaves. These classes of queries are vital for practical applications but are beyond the scope of most current neuro-symbolic models. Our approach employs an approximation scheme that facilitates acyclic traversals for cyclic patterns, thereby embedding additional symbolic bias into the query execution process. Our experimental evaluation demonstrates that our framework performs competitively on three datasets, effectively handling cyclic queries through our approximation strategy. Additionally, it maintains the performance of existing neuro-symbolic models on anchored tree-like queries and extends their capabilities to queries with existentially quantified variables.

Figures (6)

• Figure 1: (a) Edges in anchored tree-like queries are structured as trees where the leaves are anchors and the root is the target variable (here $x$); (b) leaves in tree-like queries can be anchors or existential (unanchored) variables (here $w$); (c) arbitrary pattern queries can have cycles.
• Figure 2: The triangle query $q_\Delta$ and tree-like approximations. Best viewed in color.
• Figure 3: Graph pattern queries introduced by ren2020beta and used in our experiments. (The figure is taken from zhu2022neural.)
• Figure 4: Examples of cyclic queries.
• Figure 5: Precision using 0.5 classification threshold for different depths of unravelings for the triangle query (FB15k-237).

Theorems & Definitions (11)

• Example 3.1
• Example 3.2
• Example 3.3
• Proposition 3.1
• Proposition 3.2
• Proposition 3.3
• Example A.1
• Example B.1
• Example B.2
• Example B.3