README: Topological Encoder-Decoder Framework for Temporal Graph Learning

Paper

A Topological Encoder Decoder Framework for Temporal Graph Learning

R. Buck, K. Shamsi, B. Ngo, A. Tola, B. Coskunuzer, and C. G. Akcora.

@inproceedings{buck2026topoged,
  title = {A Topological Encoder Decoder Framework for Temporal Graph Learning},
  author = {Buck, R. and Shamsi, K. and Ngo, B. and Tola, A. and Coskunuzer, B. and Akcora, C. G.},
  booktitle = {Advances in Neural Information Processing Systems},
  year = {2026},
  url = {https://openreview.net/forum?id=cZEj9pgOP7}
}

Overview

Many real-world systems—such as transaction networks, citation graphs, and online communities—evolve dynamically over time. Traditional temporal graph learning methods often struggle when new nodes appear or existing nodes disappear (node churn), turning future prediction into a complex graph reconstruction problem.

This project introduces TOPOGED (Topological Graph Encoder-Decoder), a fully inductive encoder-decoder framework designed for discrete-time temporal graph forecasting. Rather than predicting edges directly over a fixed node set, TOPOGED frames temporal graph prediction as an inverse topology problem.

Each observed snapshot is encoded as a multiscale filtration descriptor. A temporal predictor forecasts the next descriptor, node and edge budgets, and edge-type proportions. The node-memory module and phased decoder then construct a complete future snapshot for downstream node, link, and graph-property evaluation.

Open the clean framework PNG

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What We Do & How We Do It

• Multiscale Topological Encoding: We summarize each graph snapshot using a degree-based filtration descriptor $\Phi(\mathcal{G}) = (X, Y)$ that records node and induced-edge counts across cumulative thresholds.

• Budget & Probability Forecasting: A lightweight temporal predictor forecasts the next snapshot's descriptor along with overall node and edge budgets, alongside the expected fraction of newly appearing nodes.

• Arrival-Aware Node Memory: A memory module uses recency, degree, and historical frequency to sample reappearing old nodes, while new nodes are instantiated based on arrival budgets.

• Multi-Phase Edge Decoding: Edges are constructed progressively across four distinct inductive categories:

1. Old-Old Bank ($\mathcal{E}^{oo-bank}$): Recurring interactions between previously seen old nodes.

2. Old-Old Nobank ($\mathcal{E}^{oo-nobank}$): Newly formed edges between old nodes.

3. Old-New ($\mathcal{E}^{on}$): Connections bridging existing nodes and newly arrived nodes.

4. New-New ($\mathcal{E}^{nn}$): Interactions occurring exclusively among new nodes.

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Node Arrivals and Edge Types

New nodes appear for the first time in a snapshot; nodes seen in any earlier snapshot are old, including nodes that disappear and later reappear. Previously unseen edges can connect two old nodes, an old node and a new node, or two new nodes. TopoGED forecasts the number of arriving nodes, introduces unlabeled nodes, and generates their connections within the predicted budgets.

View the node-and-edge example as a PDF

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Probability Types & Distributions

To accurately distribute edge budgets across changing network environments, the framework models and projects empirical transition probabilities across the inductive edge categories ($\pi_t^{oo-bank}, \pi_t^{oo-nobank}, \pi_t^{on}, \pi_t^{nn}$). This ensures the model adapts dynamically during regime shifts instead of relying on stationary edge priors.

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Benchmarking

We rigorously evaluate performance across 14 temporal interaction datasets (including College Message, MathOverflow, Reddit-Body, TGBL-Wiki, and 10 ERC20 token Ethereum transaction networks).

TOPOGED is benchmarked against state-of-the-art temporal graph models and dynamic network architectures, including:

• ROLAND

• EvolveGCN

• VGRNN

• GC-LSTM

• HTGN

• TGCN