Neural Logic Machines (1904.11694v1)

Abstract: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

• The paper introduces Neural Logic Machines that combine neural networks with symbolic reasoning to overcome systematic generalization limitations.
• It employs tensor-based predicate representations and neural approximations of Boolean operations and quantifiers to infer complex relational rules.
• Experimental results validate scalability and strong performance across diverse tasks such as family tree reasoning, graph problems, and blocks world challenges.

Neural Logic Machines: An Overview

The paper introduces Neural Logic Machines (NLMs), which integrate the strengths of neural and symbolic methods for inductive learning and logical reasoning. NLMs aim to address the limitations of traditional neural networks, which often struggle with systematic generalization, and inductive logic programming (ILP), which suffers from scalability issues due to the complexity of searching large rule spaces. By leveraging neural networks for approximation and logic programming for relational reasoning, NLMs are designed to handle tasks that neither approach alone manages effectively.

Key Contributions and Methodology

NLMs operate over logic predicates represented as tensors, which enable them to generalize well across tasks. Through their neural-symbolic architecture, NLMs utilize three primary operations:

1. Boolean Logic Rules: These approximate logic operations (such as AND, OR, NOT) using neural networks, effectively creating lifted rules that are not tied to specific objects.
2. Quantifiers: Similarly, NLMs implement universal quantification (FOR ALL) and existential quantification (EXISTS) using neural network analogs, expanding and reducing predicates as necessary between layers.
3. Predicate Representation: By representing predicates as tensors, NLMs can operate efficiently on relational data of various orders. This capability is crucial for tasks that require examining relationships among different object sets (e.g., in the blocks world).

These operations are composed within a multi-layer architecture, with each layer processing predicates of increasing complexity. This design accommodates relational data of different arities and facilitates the deduction of complex rules incrementally, layer-by-layer.

Experimental Results

The experimental section of the paper validates the effectiveness of NLMs across several task domains, including family tree reasoning, general graph reasoning, block world problem solving, sorting, and shortest pathfinding. Key findings include:

• In family tree and graph reasoning tasks, NLMs demonstrate perfect generalization from small training instances to much larger ones.
• In relational decision-making tasks like the blocks world, NLMs manage to derive effective strategies and exhibit performance improvements over existing models such as Memory Networks and Differentiable Inductive Logic Programming.

The paper presents NLMs as not only competent at capturing complex dependencies but also remarkably scalable, overcoming a critical limitation of ILP.

Implications and Future Work

The implications of NLMs extend to multiple domains within AI, particularly where relational reasoning is pivotal. Their success suggests potential applications in areas like symbolic reasoning and decision-making, possibly impacting fields like automated theorem proving or complex system modeling.

Future enhancements could focus on adapting NLMs to handle continuous-valued inputs directly, thereby broadening their applicability. Additionally, developing methods to extract human-readable rules could bridge the interpretability gap between symbolic reasoning and neural networks, making NLMs more accessible for applications requiring transparent decision processes.

In summary, Neural Logic Machines present a robust framework for integrating neural function approximation with symbolic rule-based reasoning, achieving both the efficacy of neural networks and the structured interpretability of logic systems. Their demonstrated ability to generalize and their structure-positioned scalability represent substantial progress toward more versatile and powerful AI systems.