Neural-Symbolic Message Passing with Dynamic Pruning

TL;DR

This work tackles Complex Query Answering over incomplete Knowledge Graphs by proposing NSMP, a neural-symbolic message passing framework that integrates a pre-trained neural link predictor with symbolic reasoning via fuzzy logic. A key innovation is a dynamic pruning strategy that filters noisy messages between variable nodes, enabling efficient, interpretable reasoning for arbitrary existential first-order queries without training on complex query data. NSMP combines neural embeddings with symbolic fuzzy sets, producing interpretable variable states and achieving strong results on negative queries while delivering substantial inference-time speedups (2x to over 150x) compared to step-by-step neural-symbolic baselines. The approach is shown to be scalable and robust, with complexity analyses and ablations supporting its efficiency and effectiveness for CQA in real-world KGs.

Abstract

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) is a challenging task. Recently, a line of message-passing-based research has been proposed to solve CQA. However, they perform unsatisfactorily on negative queries and fail to address the noisy messages between variable nodes in the query graph. Moreover, they offer little interpretability and require complex query data and resource-intensive training. In this paper, we propose a Neural-Symbolic Message Passing (NSMP) framework based on pre-trained neural link predictors. By introducing symbolic reasoning and fuzzy logic, NSMP can generalize to arbitrary existential first order logic queries without requiring training while providing interpretable answers. Furthermore, we introduce a dynamic pruning strategy to filter out noisy messages between variable nodes. Experimental results show that NSMP achieves a strong performance. Additionally, through complexity analysis and empirical verification, we demonstrate the superiority of NSMP in inference time over the current state-of-the-art neural-symbolic method. Compared to this approach, NSMP demonstrates faster inference times across all query types on benchmark datasets, with speedup ranging from 2$\times$ to over 150$\times$.

Figures (5)

• Figure 1: A query graph representation of a given logical formula.
• Figure 2: A toy example to show the process of dynamic pruning. The blue arrow represents the passing of the message computed by $\varrho$, and the vector indicates the state of the corresponding node after message passing at each layer.
• Figure 3: Relative speedup of NSMP over FIT in terms of inference time on FIT datasets.
• Figure 4: Graphical representation of the query types of the BetaE dataset considered in our experiment, where $p$, $i$, $u$, and $n$ represent projection, intersection, union, and negation, respectively.
• Figure 5: Graphical representation of the query types of the FIT dataset considered in our experiment, where $l$, $m$, and $c$ represent existential leaf, multi graph, and circle, respectively.

Theorems & Definitions (12)

• Definition 3.1
• Definition 3.2
• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• proof
• proof
• Proposition 2.1
• proof
• proof