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DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs

Dongyuan Li, Shiyin Tan, Ying Zhang, Ming Jin, Shirui Pan, Manabu Okumura, Renhe Jiang

TL;DR

DyG-Mamba tackles continuous-time dynamic graph modeling by treating irregular event times as control signals that govern memory forgetting in a continuous state-space model. It redefines the SSM core components (Delta t, A, B, C) to enable timespan-aware forgetting and input-dependent robustness with spectral-norm constraints, delivering selective memory and noise filtering. The approach integrates a dynamic-graph encoding pipeline and achieves state-of-the-art results on 12 benchmarks with linear-time/space complexity relative to sequence length, offering scalable, robust long-term temporal modeling for both dynamic link prediction and node classification. This work advances practical, efficient dynamic graph modeling under irregular timestamps and varying downstream tasks.

Abstract

Dynamic graph modeling aims to uncover evolutionary patterns in real-world systems, enabling accurate social recommendation and early detection of cancer cells. Inspired by the success of recent state space models in efficiently capturing long-term dependencies, we propose DyG-Mamba by translating dynamic graph modeling into a long-term sequence modeling problem. Specifically, inspired by Ebbinghaus' forgetting curve, we treat the irregular timespans between events as control signals, allowing DyG-Mamba to dynamically adjust the forgetting of historical information. This mechanism ensures effective usage of irregular timespans, thereby improving both model effectiveness and inductive capability. In addition, inspired by Ebbinghaus' review cycle, we redefine core parameters to ensure that DyG-Mamba selectively reviews historical information and filters out noisy inputs, further enhancing the model's robustness. Through exhaustive experiments on 12 datasets covering dynamic link prediction and node classification tasks, we show that DyG-Mamba achieves state-of-the-art performance on most datasets, while demonstrating significantly improved computational and memory efficiency. Code is available at https://github.com/Clearloveyuan/DyG-Mamba.

DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs

TL;DR

DyG-Mamba tackles continuous-time dynamic graph modeling by treating irregular event times as control signals that govern memory forgetting in a continuous state-space model. It redefines the SSM core components (Delta t, A, B, C) to enable timespan-aware forgetting and input-dependent robustness with spectral-norm constraints, delivering selective memory and noise filtering. The approach integrates a dynamic-graph encoding pipeline and achieves state-of-the-art results on 12 benchmarks with linear-time/space complexity relative to sequence length, offering scalable, robust long-term temporal modeling for both dynamic link prediction and node classification. This work advances practical, efficient dynamic graph modeling under irregular timestamps and varying downstream tasks.

Abstract

Dynamic graph modeling aims to uncover evolutionary patterns in real-world systems, enabling accurate social recommendation and early detection of cancer cells. Inspired by the success of recent state space models in efficiently capturing long-term dependencies, we propose DyG-Mamba by translating dynamic graph modeling into a long-term sequence modeling problem. Specifically, inspired by Ebbinghaus' forgetting curve, we treat the irregular timespans between events as control signals, allowing DyG-Mamba to dynamically adjust the forgetting of historical information. This mechanism ensures effective usage of irregular timespans, thereby improving both model effectiveness and inductive capability. In addition, inspired by Ebbinghaus' review cycle, we redefine core parameters to ensure that DyG-Mamba selectively reviews historical information and filters out noisy inputs, further enhancing the model's robustness. Through exhaustive experiments on 12 datasets covering dynamic link prediction and node classification tasks, we show that DyG-Mamba achieves state-of-the-art performance on most datasets, while demonstrating significantly improved computational and memory efficiency. Code is available at https://github.com/Clearloveyuan/DyG-Mamba.
Paper Structure (29 sections, 3 theorems, 30 equations, 9 figures, 17 tables, 3 algorithms)

This paper contains 29 sections, 3 theorems, 30 equations, 9 figures, 17 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Methodology
  5. Dynamic Graph Encoding
  6. DyG-Mamba: Dynamic Graph Mamba
  7. Rethinking SSM on Dynamic Graph
  8. Timespan-Informed Continuous SSM
  9. DyG-Mamba for Downstream Tasks
  10. Experiments
  11. Experimental Setup
  12. Effectiveness Evaluation
  13. Efficiency Evaluation
  14. Training Efficiency
  15. Robustness Evaluation
  16. ...and 14 more sections

Key Result

Theorem 4.1

Let $\bm{A}_{k}$=$\mathrm{diag}(\lambda_{1},\ldots,\lambda_{n})$, where the real parts of the eigenvalues satisfy $\mathrm{Re}(\lambda_i)<0$. For any timespan $\Delta t_{k}$, we have $\overline{\bm{A}}_{k}$=$\mathrm{diag}(e^{\lambda_1\Delta t_{k,1}}, \ldots, e^{\lambda_n\Delta t_{k,n}})$ and $\overl

Figures (9)

  • Figure 1: Overview of our proposed DyG-Mamba with four redefined core parameters $\bm{\Delta}$, $\bm{A}$, $\bm{B}$ and $\bm{C}$. Pseudocodes are in Appendix \ref{['sec:algorithm']}.
  • Figure 2: AP score w.r.t. varying sequence lengths.
  • Figure 3: Comparison of efficiency and effectiveness.
  • Figure 4: Speed and memory comparison of two layers DyGFormer and DyG-Mamba with varying lengths.
  • Figure 5: Inserting noisy edges from 10% to 60%.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Theorem 4.1
  • Theorem 4.2
  • Theorem 4.3
  • proof
  • proof
  • proof