Brain-inspired Chaotic Graph Backpropagation for Large-scale Combinatorial Optimization

TL;DR

This paper introduces a brain-inspired chaotic backpropagation algorithm for graph neural networks, significantly improving large-scale combinatorial optimization by leveraging chaotic dynamics for better global learning.

Contribution

The paper proposes a novel chaotic training algorithm, CGBP, inspired by brain dynamics, which enhances GNN optimization for large-scale combinatorial problems.

Findings

CGBP outperforms existing GNN algorithms on benchmark datasets.

CGBP surpasses state-of-the-art methods in solving large-scale COPs.

CGBP can be integrated into existing GNN methods as a plug-in.

Abstract

Graph neural networks (GNNs) with unsupervised learning can solve large-scale combinatorial optimization problems (COPs) with efficient time complexity, making them versatile for various applications. However, since this method maps the combinatorial optimization problem to the training process of a graph neural network, and the current mainstream backpropagation-based training algorithms are prone to fall into local minima, the optimization performance is still inferior to the current state-of-the-art (SOTA) COP methods. To address this issue, inspired by possibly chaotic dynamics of real brain learning, we introduce a chaotic training algorithm, i.e. chaotic graph backpropagation (CGBP), which introduces a local loss function in GNN that makes the training process not only chaotic but also highly efficient. Different from existing methods, we show that the global ergodicity and pseudo-randomness of such chaotic dynamics enable CGBP to learn each optimal GNN effectively and globally, thus solving the COP efficiently. We have applied CGBP to solve various COPs, such as the maximum independent set, maximum cut, and graph coloring. Results on several large-scale benchmark datasets showcase that CGBP can outperform not only existing GNN algorithms but also SOTA methods. In addition to solving large-scale COPs, CGBP as a universal learning algorithm for GNNs, i.e. as a plug-in unit, can be easily integrated into any existing method for improving the performance.