Contrastive learning for supervised graph matching

Deep graph matching techniques have shown promising results in recent years. In this work, we cast deep graph matching as a contrastive learning task and introduce a new objective function for contrastive mapping to exploit the relationships between matches and non-matches. To this end, we develop a hardness attention mechanism to select negative samples which captures the relatedness and informativeness of positive and negative samples. Further, we propose a novel deep graph matching framework, Stable Graph Matching (StableGM), which incorporates Sinkhorn ranking into a stable marriage algorithm to efficiently compute one-to-one node correspondences between graphs. We prove that the proposed objective function for contrastive matching is both positive and negative informative, offering theoretical guarantees to achieve dual-optimality in graph matching. We empirically verify the effectiveness of our proposed approach by conducting experiments on standard graph matching benchmarks.