Mathematical expression exploration with graph representation and generative graph neural network.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Mathematics

Background:

• Symbolic Regression (SR) traditionally uses tree representations, which can be redundant.
• Deep learning has advanced tree-centric SR, but graph-based deep learning for SR is underexplored.
• Computation graphs offer a more succinct representation of mathematical expressions than trees.

Purpose of the Study:

• To introduce a novel deep learning approach for Symbolic Regression using Directed Acyclic Graphs (DAGs).
• To leverage generative graph neural networks for efficient and intuitive mathematical expression discovery.
• To address the limitations of redundant substructures in tree-based SR methods.

Main Methods:

• Proposed Graph-based Deep Symbolic Regression (GraphDSR) using DAG representation.
• Employed generative graph neural networks to incrementally construct DAGs.
• Utilized vectorized node types and adjacency matrices for graph representation.
• Incorporated validity checks and domain-agnostic constraints to guide the search process.
• Optimized constants with SGD and BFGS, and refined the neural network with reinforcement learning.

Main Results:

• Demonstrated the effectiveness of GraphDSR across 110 diverse benchmarks.
• Achieved potent results, highlighting the advantages of DAG representation in SR.
• Showcased the capability of graph neural networks in generating coherent mathematical expressions.

Conclusions:

• GraphDSR presents a powerful and efficient alternative to traditional tree-based SR methods.
• The DAG representation combined with generative graph neural networks significantly enhances SR performance.
• This approach opens new avenues for deep learning applications in symbolic regression and automated scientific discovery.