HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems

Graph neural networks (GNNs) have shown promising performance in solving both Boolean satisfiability (SAT) and Maximum Satisfiability (MaxSAT) problems due to their ability to efficiently model and capture the structural dependencies between literals and clauses. However, GNN methods for solving Weighted MaxSAT problems remain underdeveloped. The challenges arise from the non-linear dependency and sensitive objective function, which are caused by the non-uniform distribution of weights across clauses. In this paper, we present HyperSAT, a novel neural approach that employs an unsupervised hypergraph neural network model to solve Weighted MaxSAT problems. We propose a hypergraph representation for Weighted MaxSAT instances and design a cross-attention mechanism along with a shared representation constraint loss function to capture the logical interactions between positive and negative literal nodes in the hypergraph. Extensive experiments on various Weighted MaxSAT datasets demonstrate that HyperSAT achieves better performance than state-of-the-art competitors.

A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction

In this paper, we consider the problem of inferring the sign of a link based on limited sign data in signed networks. Regarding this link sign prediction problem, SDGNN (Signed Directed Graph Neural Networks) provides the best prediction performance currently to the best of our knowledge. In this paper, we propose a different link sign prediction architecture call SELO (Subgraph Encoding via Linear Optimization), which obtains overall leading prediction performances compared the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization method. Comprehensive experiments are conducted on six real-world signed networks with AUC, F1, micro-F1, and Macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the six real-world networks and in all the four evaluation metrics.