Adaptive Memory Retention in Dynamic Graphs

Modeling graphs demands a careful balance between long-range propagation of information across nodes and the controlled dissipation of noisy or redundant signals to ensure stable learning and generalization. This challenge is exacerbated in dynamic graphs, where structural and temporal information interact, leading to uncontrolled information accumulation and amplifying noise, thereby affecting generalization. We introduce LAMP, a dynamic graph model for snapshot-based dynamic graphs that incorporates adaptive, learned dissipation within a principled dynamical systems framework. Our architecture combines impulsive neural ODEs with an antisymmetric parameterization to model conservative information flow, alongside data-driven dissipative dynamics that regulate information retention over space and time. This formulation yields stable yet expressive representations and enables effective long-range dependency modeling while avoiding pathological information buildup. We provide a theoretical analysis establishing stability guarantees and characterizing the representational power. Extensive experiments on synthetic and real-world benchmarks demonstrate state-of-the-art performance, particularly on tasks requiring extended-range dependency modeling.

Many real-world systems can be viewed as networks that change over time. Examples include road traffic, disease spread, social interactions, and communication systems. Learning from these changing networks is difficult because useful information may need to travel across many steps in both the network and time, while irrelevant or noisy information should be forgotten. This paper introduces LAMP, a new machine learning model designed to handle this balance. LAMP learns how much past information to keep and how much to filter out as a network evolves. This helps the model remember important long-term patterns without letting noise build up. We also introduce new tests that specifically measure whether models can track information over long distances and long time periods. Across these tests and several real-world tasks, LAMP performs better than or competitively with existing methods. The results suggest that learning when to remember and when to forget is important for building reliable models of changing networks.