NEU: Continuous-time memory evolution for temporal interaction graph networks.

Abstract

Graph neural networks (GNNs) have become a cornerstone for modeling complex relational data, yet most canonical architectures assume the graph topology is static. In real-world temporal interaction graphs (TIGs), however, nodes and edges evolve continuously. Recent memory-augmented temporal GNNs address this by maintaining a learnable memory for every node, which is discretely updated only when an interaction occurs. Although memory based models such as TGN and TGAT include time encoding as a marker representing the update time of node memory, the elapsed time merely serves as a static input feature that modulates the next embedding update. The memory itself is still assumed to remain unchanged between two events, implying that the node state evolves through a sequence of instantaneous jumps. This event-driven assumption neglects two key temporal phenomena: (1) natural decay-a node's latent state gradually loses relevance during long inactivity; and (2) short-term drift-the latest neighbour exerts a residual influence that fades smoothly rather than abruptly. Consequently, memories of sparsely active nodes become stale. We can only obtain the memory of the node at the time of the event, but cannot obtain the memory at any given time. The discrete-update paradigm cannot infer a node's state at arbitrary intermediate timestamps, limiting both accuracy and temporal consistency. To tackle these limitations, we introduce the Natural Evolution Unit (NEU), a module that inserts a continuous-time memory evolution stage before the embedding read-out. NEU treats the time difference not as an auxiliary input but as a dynamic driver of a learnable ordinary differential equation, enabling memory to drift and decay smoothly between events. This brings two benefits: (1) node states become continuously queryable at arbitrary timestamps, providing continuous time inferability and interpretability; and (2) our modeling of time differences has been upgraded from "static input" to "dynamic evolution driven", allowing the ODE-driven dynamics to dominate the temporal modeling and reducing dependence on learnable time encoding. Therefore, we adopt a fixed time encoding to control the stability of training, thereby further improving the experimental results. We conducted comprehensive experiments on five public datasets, and the results showed that NEU consistently improved AUC and AP on the strongest memory based baseline. This indicates that our method is crucial for mitigating memory aging and enhancing long-term prediction, offering a simple yet effective new perspective for representation learning on dynamic graphs.