# Learning Long Range Spatio-Temporal Representations over Continuous Time Dynamic Graphs with State Space Models

arXiv: https://arxiv.org/abs/2606.04672 · HTML: https://mlsanity.com/paper/2606.04672/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Towards Better Dynamic Graph Learning: New Architecture and Unified Library](https://mlsanity.com/paper/2303.13047/) (2023)
- [Do We Really Need Complicated Model Architectures For Temporal Networks?](https://mlsanity.com/paper/2302.11636/) (2023)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Towards Better Evaluation for Dynamic Link Prediction](https://mlsanity.com/paper/2207.10128/) (2022)
- [TCL: Transformer-based Dynamic Graph Modelling via Contrastive Learning](https://mlsanity.com/paper/2105.07944/) (2021)
- [Provably expressive temporal graph networks](https://mlsanity.com/paper/2209.15059/) (2022)
- [Realistic Synthetic Financial Transactions for Anti-Money Laundering Models](https://mlsanity.com/paper/2306.16424/) (2023)
- [Long Range Propagation on Continuous-Time Dynamic Graphs](https://mlsanity.com/paper/2406.02740/) (2024)
- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)
- [State Space Models on Temporal Graphs: A First-Principles Study](https://mlsanity.com/paper/2406.00943/) (2024)
- [Representation Learning over Dynamic Graphs](https://mlsanity.com/paper/1803.04051/) (2018)
- [DyGMamba: Efficiently Modeling Long-Term Temporal Dependency on Continuous-Time Dynamic Graphs with State Space Models](https://mlsanity.com/paper/2408.04713/) (2024)

## Abstract (arXiv)

Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.