Differentiable Koopman Operator for Contrastive Learning on Dynamic Graphs

2026-10-02

AI Summary

This study addresses the vulnerability of dynamic graph contrastive learning to distribution shifts caused by the absence of explicit evolutionary modeling, and proposes the KAIROS framework. To our knowledge, this work is the first to introduce differentiable Koopman operators into dynamic graph contrastive learning, enabling explicit modeling of node representations and the disentanglement of anomalous prediction residuals by linearizing temporal evolution in the embedding space. Furthermore, the framework incorporates a dual-view encoder, graph diffusion structural views, and multi-granularity temporal window contrastive objectives for self-supervised optimization. Extensive experiments on nine benchmark datasets demonstrate that KAIROS achieves state-of-the-art anomaly detection performance, improving ROC-AUC by up to 23.15 points, while also delivering superior results in unsupervised node classification tasks.

Abstract

Real-world interaction networks are inherently dynamic: edges form and dissolve as node behavior shifts over time. Most snapshot-based contrastive methods encode temporal dependencies implicitly in encoder weights, without an explicit model of how node representations evolve, making them brittle under distribution shifts. We propose KAIROS (Koopman-Aligned Invariant Representations for Open Dynamic Systems), a self-supervised framework that embeds a differentiable Koopman operator within a dynamic graph contrastive learning loop to linearize temporal evolution in the learned embedding space. A dual-view encoder pairs raw node features with a graph-diffused structural view and is optimized with multi-granularity contrastive objectives across temporal windows. For anomaly detection, KAIROS uses the Koopman prediction residual together with temporal inconsistency and local neighborhood deviation to separate irregular behavior from predictable graph evolution. Evaluated on nine dynamic graph benchmarks, KAIROS achieves state-of-the-art anomaly detection results on all nine datasets, with gains of up to 23.15 ROC-AUC points over prior work, while remaining competitive for unsupervised node classification. These results show that explicit dynamics modeling provides a scalable and effective inductive bias for temporal graph representation learning.

Problem

• Dynamic Graphs
• Contrastive Learning
• Distribution Shift
• Anomaly Detection
• Temporal Evolution

Innovation

• Differentiable Koopman Operator
• Dynamic Graph Contrastive Learning
• Anomaly Detection
• Self-supervised Learning
• Temporal Evolution