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Revisiting Node Affinity Prediction in Temporal Graphs

Krishna Sri Ipsit Mantri, Or Feldman, Moshe Eliasof, Chaim Baskin

TL;DR

The paper tackles future node affinity prediction in continuous-time dynamic graphs, where standard TGNNs underperform simple heuristics like Persistent Forecast and Moving Average. It reveals a theoretical link between these heuristics and linear state-space models, and introduces NAViS, a TGNN variant that uses per-node states plus a global virtual state and a rank-aware loss to better capture temporal dynamics and ranking quality. NAViS consistently outperforms both heuristics and prior TGNNs on the Temporal Graph Benchmark (TGB) and additional link-prediction datasets, illustrating improved ranking accuracy and generalization. The work highlights the importance of aligning model inductive biases and training objectives with the task, suggesting that linear-SMM-inspired architectures with global context and ranking-focused losses offer practical and scalable gains for dynamic graph forecasting.

Abstract

Node affinity prediction is a common task that is widely used in temporal graph learning with applications in social and financial networks, recommender systems, and more. Recent works have addressed this task by adapting state-of-the-art dynamic link property prediction models to node affinity prediction. However, simple heuristics, such as Persistent Forecast or Moving Average, outperform these models. In this work, we analyze the challenges in training current Temporal Graph Neural Networks for node affinity prediction and suggest appropriate solutions. Combining the solutions, we develop NAViS - Node Affinity prediction model using Virtual State, by exploiting the equivalence between heuristics and state space models. While promising, training NAViS is non-trivial. Therefore, we further introduce a novel loss function for node affinity prediction. We evaluate NAViS on TGB and show that it outperforms the state-of-the-art, including heuristics. Our source code is available at https://github.com/orfeld415/NAVIS

Revisiting Node Affinity Prediction in Temporal Graphs

TL;DR

The paper tackles future node affinity prediction in continuous-time dynamic graphs, where standard TGNNs underperform simple heuristics like Persistent Forecast and Moving Average. It reveals a theoretical link between these heuristics and linear state-space models, and introduces NAViS, a TGNN variant that uses per-node states plus a global virtual state and a rank-aware loss to better capture temporal dynamics and ranking quality. NAViS consistently outperforms both heuristics and prior TGNNs on the Temporal Graph Benchmark (TGB) and additional link-prediction datasets, illustrating improved ranking accuracy and generalization. The work highlights the importance of aligning model inductive biases and training objectives with the task, suggesting that linear-SMM-inspired architectures with global context and ranking-focused losses offer practical and scalable gains for dynamic graph forecasting.

Abstract

Node affinity prediction is a common task that is widely used in temporal graph learning with applications in social and financial networks, recommender systems, and more. Recent works have addressed this task by adapting state-of-the-art dynamic link property prediction models to node affinity prediction. However, simple heuristics, such as Persistent Forecast or Moving Average, outperform these models. In this work, we analyze the challenges in training current Temporal Graph Neural Networks for node affinity prediction and suggest appropriate solutions. Combining the solutions, we develop NAViS - Node Affinity prediction model using Virtual State, by exploiting the equivalence between heuristics and state space models. While promising, training NAViS is non-trivial. Therefore, we further introduce a novel loss function for node affinity prediction. We evaluate NAViS on TGB and show that it outperforms the state-of-the-art, including heuristics. Our source code is available at https://github.com/orfeld415/NAVIS

Paper Structure

This paper contains 19 sections, 3 theorems, 18 equations, 2 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Our contributions.
  3. Background
  4. Beyond Moving Average.
  5. Method
  6. What Hinders TGNNs in Future Node Affinity Prediction
  7. NAViS: Node Affinity Prediction with a Global Virtual State
  8. Learning with Rank-Based Loss: Why Cross-Entropy Fails
  9. Experiments
  10. Node Affinity Prediction on TGB
  11. Generalization to Link Prediction Datasets
  12. Ablation study
  13. Related Work
  14. Conclusion
  15. Datasets statistics and description
  16. ...and 4 more sections

Key Result

Theorem 1

Let $\mathcal{H}$ be the set of basic heuristics (PF, SMA, EMA), $\mathcal{F}_{\mathrm{lin\text{-}SSM}}$ be the set of maps realizable by the linear SSM in Equation eq:ssm_state and Equation eq:ssm_output. Then, the following strict inclusion holds:

Figures (2)

  • Figure 1: Synthetic node affinity experiment. Node affinities depend on a global, regime-switching latent $g(t)$ with nonlinear component $g(t)^2$ and node-specific phases. Baselines relying only on per-node histories (Persistent Forecast, SMA, EMA) or a local AR(1) SSM cannot recover the shared latent, leading to higher error. Ours, indicating NAViS, maintains a virtual global state, achieves the lowest error on both metrics. In \ref{['app:teaser']} we provide the full experiment details and baseline descriptions.
  • Figure 2: NAViS architecture for node affinity prediction. The current state and previous affinity vector are projected through linear transformations and aggregated into a new state. A lightweight gated mechanism ensures a persistent, linear input–output. The predicted affinity vector is then produced directly from this state based on the virtual global state.

Theorems & Definitions (6)

  • Theorem 1: Linear SSMs generalize basic heuristics
  • proof
  • Theorem 2
  • proof
  • Theorem 3: Cross-Entropy is Suboptimal for Ranking
  • proof