Negative Metric Learning for Graphs

TL;DR

NML-GCL addresses false negatives in graph contrastive learning by integrating a learnable Negative Metric Network to form a negative metric space. A bi-level optimization scheme jointly trains the encoder and NMN using self-supervision, yielding a tighter mutual information bound than InfoNCE and enabling mutual reinforcement between components. Theoretical analysis proves improved MI bounds and the ability to distinguish false negatives, while experiments on six benchmarks demonstrate consistent downstream gains and effective false-negative identification. This approach offers a data-driven, principled way to refine negative sampling in GCL, with practical impact on node classification and clustering tasks.

Abstract

Graph contrastive learning (GCL) often suffers from false negatives, which degrades the performance on downstream tasks. The existing methods addressing the false negative issue usually rely on human prior knowledge, still leading GCL to suboptimal results. In this paper, we propose a novel Negative Metric Learning (NML) enhanced GCL (NML-GCL). NML-GCL employs a learnable Negative Metric Network (NMN) to build a negative metric space, in which false negatives can be distinguished better from true negatives based on their distance to anchor node. To overcome the lack of explicit supervision signals for NML, we propose a joint training scheme with bi-level optimization objective, which implicitly utilizes the self-supervision signals to iteratively optimize the encoder and the negative metric network. The solid theoretical analysis and the extensive experiments conducted on widely used benchmarks verify the superiority of the proposed method.

Figures (7)

• Figure 1: Illustration of GCL with false negatives and NML enhanced GCL.
• Figure 2: Overview of NML-GCL. First, NML-GCL generates two contrastive views $\mathcal{G}_U$ and $\mathcal{G}_V$ based on the initial graph $\mathcal{G}$. Then NML-GCL employs a bi-level optimization to iteratively training GCN $E$ and NMN $M$. In $(t+1)$-th iteration, NML-GCL first updates $M$ to $M^{(t+1)}$ under the guidance of GCN $E^{(t)}$ in previous iteration, then uses $M^{(t+1)}$ to obtain the new negative metric matrix $\mathbf{M}^{(t+1)}$ based on the node embeddings $\mathbf{U}^{(t)}$ and $\mathbf{V}^{(t)}$ in contrastive views, and finally, updates GCN $E$ to $E^{(t+1)}$ under the guidance of $\mathbf{M}^{(t+1)}$.
• Figure 3: Visualization of node clustering on Computers.
• Figure 4: Hyper-parameter analysis.
• Figure 5: Predicted weights of False Negatives (FN) and True Negatives (TN) during training of NML-GCL.

Theorems & Definitions (5)

• Definition 1: False Negatives
• Theorem 1
• Theorem 2
• proof
• proof