Annealing Machine-assisted Learning of Graph Neural Network for Combinatorial Optimization

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still scaling limitations. In parallel, Graph Neural Networks (GNN) have been recently adapted to solve combinatorial problems, showing competitive results and potentially high scalability due to their distributed nature. We propose a merging approach that aims at retaining both the accuracy exhibited by AMs and the representational flexibility and scalability of GNNs. Our model considers a compression step, followed by a supervised interaction where partial solutions obtained from the AM are used to guide local GNNs from where node feature representations are obtained and combined to initialize an additional GNN-based solver that handles the original graph's target problem. Intuitively, the AM can solve the combinatorial problem indirectly by infusing its knowledge into the GNN. Experiments on canonical optimization problems show that the idea is feasible, effectively allowing the AM to solve size problems beyond its original limits.

EdgePruner: Poisoned Edge Pruning in Graph Contrastive Learning

Graph Contrastive Learning (GCL) is unsupervised graph representation learning that can obtain useful representation of unknown nodes. The node representation can be utilized as features of downstream tasks. However, GCL is vulnerable to poisoning attacks as with existing learning models. A state-of-the-art defense cannot sufficiently negate adverse effects by poisoned graphs although such a defense introduces adversarial training in the GCL. To achieve further improvement, pruning adversarial edges is important. To the best of our knowledge, the feasibility remains unexplored in the GCL domain. In this paper, we propose a simple defense for GCL, EdgePruner. We focus on the fact that the state-of-the-art poisoning attack on GCL tends to mainly add adversarial edges to create poisoned graphs, which means that pruning edges is important to sanitize the graphs. Thus, EdgePruner prunes edges that contribute to minimizing the contrastive loss based on the node representation obtained after training on poisoned graphs by GCL. Furthermore, we focus on the fact that nodes with distinct features are connected by adversarial edges in poisoned graphs. Thus, we introduce feature similarity between neighboring nodes to help more appropriately determine adversarial edges. This similarity is helpful in further eliminating adverse effects from poisoned graphs on various datasets. Finally, EdgePruner outputs a graph that yields the minimum contrastive loss as the sanitized graph. Our results demonstrate that pruning adversarial edges is feasible on six datasets. EdgePruner can improve the accuracy of node classification under the attack by up to 5.55% compared with that of the state-of-the-art defense. Moreover, we show that EdgePruner is immune to an adaptive attack.