Nonlinear Correct and Smooth for Semi-Supervised Learning

Graph-based semi-supervised learning (GSSL) has been used successfully in various applications. Existing methods leverage the graph structure and labeled samples for classification. Label Propagation (LP) and Graph Neural Networks (GNNs) both iteratively pass messages on graphs, where LP propagates node labels through edges and GNN aggregates node features from the neighborhood. Recently, combining LP and GNN has led to improved performance. However, utilizing labels and features jointly in higher-order graphs has not been explored. Therefore, we propose Nonlinear Correct and Smooth (NLCS), which improves the existing post-processing approach by incorporating non-linearity and higher-order representation into the residual propagation to handle intricate node relationships effectively. Systematic evaluations show that our method achieves remarkable average improvements of 13.71% over base prediction and 2.16% over the state-of-the-art post-processing method on six commonly used datasets. Comparisons and analyses show our method effectively utilizes labels and features jointly in higher-order graphs to resolve challenging graph relationships.

RELS-DQN: A Robust and Efficient Local Search Framework for Combinatorial Optimization

Combinatorial optimization (CO) aims to efficiently find the best solution to NP-hard problems ranging from statistical physics to social media marketing. A wide range of CO applications can benefit from local search methods because they allow reversible action over greedy policies. Deep Q-learning (DQN) using message-passing neural networks (MPNN) has shown promise in replicating the local search behavior and obtaining comparable results to the local search algorithms. However, the over-smoothing and the information loss during the iterations of message passing limit its robustness across applications, and the large message vectors result in memory inefficiency. Our paper introduces RELS-DQN, a lightweight DQN framework that exhibits the local search behavior while providing practical scalability. Using the RELS-DQN model trained on one application, it can generalize to various applications by providing solution values higher than or equal to both the local search algorithms and the existing DQN models while remaining efficient in runtime and memory.