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Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective
Luis C. Lamb, Artur Garcez, Marco Gori, Marcelo Prates, Pedro Avelar, Moshe Vardi
TL;DR
AI systems need richer reasoning to become semantically sound, explainable, and reliable, motivating neural-symbolic approaches. This paper surveys neural-symbolic computing and GNNs, analyzes their relationship and applications, and identifies future evaluation and application directions.
Problem
Existing surveys had not specifically reviewed the relationship between GNNs and neural-symbolic computing, despite the need for semantically sound, explainable, and reliable AI systems.
Method
The paper synthesizes neural-symbolic computing approaches and GNN models, architectures, applications, and relationships to relational and symbolic learning.
Results
The review identifies a productive relationship between GNNs and neural-symbolic computing across combinatorial optimization, constraint satisfaction, relational reasoning, and other AI and computer-science problems.
Takeaways & Limitations
Principled integration of GNNs and neural-symbolic computing is presented as a richer alternative for constructing trustful, explainable, and robust AI systems.
Takeaways & Limitations
Future work requires application and systematic evaluation on specific tasks and datasets.
Abstract
from arXiv · showhide
Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.
1 Introduction
Richer AI systems are presented as requiring a sound reasoning layer alongside deep learning for semantic soundness, explainability, and reliability. The paper surveys neural-symbolic computing and examines GNNs’ relationship to it, addressing a gap in prior surveys.
- Richer AI systems require a sound reasoning layer alongside deep learning to support semantic soundness, explainability, and reliability.
- The paper surveys neural-symbolic computing approaches for knowledge representation and reasoning within deep learning.
- It also reviews GNNs for learning and reasoning about problems requiring relational structures or symbolic learning.
- Prior GNN surveys did not focus on the relationship between GNNs and neural-symbolic computing.
- The paper’s stated contribution is to review and analyse recent results on the specific relationship between GNNs and NSC and outline research directions combining them.
2 Neural-Symbolic Computing Taxonomy
The taxonomy organizes neural-symbolic systems by how symbolic representations and reasoning interact with neural networks. The paper positions GNNs and rich embeddings as relevant to structured reasoning, while identifying Type 6 systems as a research target amid a learning–reasoning tension.
- Kautz’s taxonomy outlines six neural-symbolic system types, ranging from symbolic-neural integration to NEURO[SYMBOLIC].
- GNNs and neural-symbolic computing both enrich neural-network input representations, progressing from tree structures to graphs.
- Type 1 systems use symbolic inputs or outputs with standard deep learning, including language translation and question answering.
- Type 4 systems compile symbolic knowledge into neural-network training or architecture, whereas Type 5 maps logic rules into embeddings that act as soft loss constraints.
- Type 6 systems aim for true symbolic reasoning inside a neural engine and combinatorial reasoning, potentially using attention mechanisms or GNNs.
- The paper proposes combining rich logic embeddings with GNN attention mechanisms or convolutions toward sound Type 6 systems, while noting tension between effective learning and sound reasoning.
3 Graph Neural Networks Meet Neural-Symbolic Computing
The section presents neural architectures and symbolic representations that support learning over relational structures. It emphasizes tensorized logic, pointer-based combinatorial reasoning, and graph convolutions that accommodate permutation-invariant, variable-sized, non-grid inputs.
- 3.1 Logic Tensor Networks: Tensorisation embeds first-order logic symbols, including constants, facts, and rules, into real-valued tensors for neural computation.Constants are typically one-hot vectors, while predicates and functions use matrices or higher-order tensors.
- 3.1 Logic Tensor Networks: Logic Tensor Networks extend Neural Tensor Networks to represent more complex first-order logic formulas and use symbolic information as a learning prior.
- 3.2 Pointer Networks: Pointer Networks decode probability distributions over input-element indices, enabling outputs defined over variable-sized input sets.Their pointers support loss functions for combinatorial optimization, including Traveling Salesperson, Delaunay Triangulation, and Convex Hull problems.
- 3.2 Pointer Networks: Pointer Networks cannot be directly applied to general non-complete graphs, despite solving problems defined over sets.
- 3.4 Graph Convolutional Networks: Graph convolutions extend neural learning to graph inputs, which naturally represent symbolic expressions and support permutation invariance and generalization across input sizes.Their aggregation is adjacency-masked, making graph convolution a generalization of attention for non-complete graphs.
- 3.4 Graph Convolutional Networks: Graph Convolutional Networks generalize convolutional networks from grid topologies to non-grid graphs by transforming and aggregating vertex representations.Unlike grid convolutions, GCNs cannot rely on fixed spatial kernels because general graphs have variable neighbor counts and no canonical relative positions.
4 Perspectives and Applications of GNNs to Neural-Symbolic Computing
GNNs are applied across relational, visual, language, software, optimization, and constraint-solving tasks, while attention-equipped GNNs are proposed for richer neural-symbolic reasoning.
- Attention-equipped GNNs are proposed as a promising direction for rich reasoning and learning in type 6 neural-symbolic systems.The paper identifies systematic evaluation on specific tasks and datasets as future work.
- Relational reasoning: Hybrid CNN + GNN models support human-object interaction understanding, object localization, and visual question answering.
- Natural language processing: Graph formulations improve upon state-of-the-art seq2seq models for text cooccurrence tasks and support knowledge-base link prediction.
- Software engineering: GNN variants have been used to analyze graph representations of programs in software engineering.Program graphs can be derived unambiguously through parsing because code is structured and unambiguous.
- Combinatorial optimization: GNN-based models target combinatorial optimization problems including Minimum Vertex Cover, Maximum Cut, and Traveling Salesperson.These models embed graphs for heuristic search or learn end-to-end solutions.
- Constraint satisfaction: Neural-symbolic GNN solvers have been proposed for decision variants of SAT, TSP, and graph colouring, with training using a single supervision bit per instance.Some models can extract assignments from the trained model.
5 Conclusions
The paper reviews the relationship between GNNs and neural-symbolic computing, highlighting applications across foundational and applied problems and the value of principled integration for AI systems.
- The review covers GNN and neural-symbolic computing research spanning combinatorial optimization, constraint satisfaction, relational reasoning, language, life sciences, and vision.The paper attributes this breadth partly to the natural representation of many learning tasks as graphs.
- Principled integration of GNNs and neural-symbolic computing offers a richer alternative for constructing trustful, explainable, and robust AI systems.