Graph Rule Learning With Differentiable MAX-SAT Reasoning
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Solution Overview
Problem
Existing graph-based machine learning approaches, such as neural networks, lack high-level reasoning abilities and require manual adaptation for different applications, limiting their applicability and explainability.
Innovation Solution
A method that combines graph representations with a differentiable satisfiability solver to learn and apply logical rules by defining a maximum satisfiability (MAX-SAT) problem, estimating gradients, and mapping features to intermediate vector representations, enabling flexible application across various domains without manual adaptation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If neural networks such as GNNs, GCNs, and GATs are used for graph-based machine learning, then performance in application domains is improved, but high-level reasoning abilities and explainability deteriorate
Solution Approach 1:
The patent segments the learning process into two distinct components: a differentiable SAT solver that learns logical rules and a gradient estimator that optimizes the mapping from input features to SAT variables. This segmentation allows each component to specialize - the SAT solver provides explainable logical rules while the gradient estimator enables learning - thereby resolving the contradiction between performance and interpretability
Solution Approach 2:
The patent introduces an intermediate representation layer that maps input features to variables in a SAT formula. This intermediary layer acts as a bridge between the neural network input and the logical reasoning component, allowing gradients to flow through the mapping while preserving the interpretability of the learned SAT rules. The intermediate representation enables both high-level reasoning and explainability to coexist
2Loss of time
If traditional machine learning approaches are used, then learning speed is improved, but adaptability to different applications deteriorates
Solution Approach 1:
The patent creates a universal framework that can be applied to any graph-based machine learning task by formulating the problem as a SAT learning task. The differentiable SAT solver and gradient estimator constitute a general-purpose system that adapts to different applications through the problem formulation rather than requiring manual adaptation, thereby achieving both fast learning and high adaptability
Solution Approach 2:
The patent enables adaptability through parameter changes in the SAT formula and the mapping function. By adjusting the SAT variables, constraints, and the feature-to-variable mapping, the same core architecture can solve different graph-based learning problems across various domains without redesigning the entire system
Data Source
AI summary
A machine learning method for learning and applying a rule set from relational data includes receiving a graph representing relational data, wherein nodes represent elements of the graph, and edges represent relationships between nodes, and generating an intermediate representation of the graph by mapping features of the nodes and edges of the graph to an intermediate vector representation. Optimized logical rules that define the nodes and edges of the graph based on the intermediate vector representation are learned by: defining a maximum satisfiability (MAX-SAT) problem for the graph; and estimating a gradient around a solution of the MAX-SAT problem to produce the optimized logical rules, which are applied to a new graph. The data can be medical data and the graph can be used in a machine-learning task, such as using the medical data for disease prediction, for optimization of the machine-learning task and/or to support decision-making.