# Inferring Network Evolutionary History via Structure-State Coupled Learning

arXiv: https://arxiv.org/abs/2601.02121 · HTML: https://mlsanity.com/paper/2601.02121/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Builds on (most cited first, 20 of 20)

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- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
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- [Reconstructing the evolution history of networked complex systems](https://mlsanity.com/paper/2403.14983/) (2024)
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- [ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks](https://mlsanity.com/paper/2203.00653/) (2022)
- [A Diffusive Data Augmentation Framework for Reconstruction of Complex Network Evolutionary History](https://mlsanity.com/paper/2501.06485/) (2025)
- [Beyond Equilibrium: Non-Equilibrium Foundations Should Underpin Generative Processes in Complex Dynamical Systems](https://mlsanity.com/paper/2505.18621/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel k-means, and Heat Kernel](https://mlsanity.com/paper/2203.09888/) (2022)

## Abstract (arXiv)

Inferring a network's evolutionary history from a single final snapshot with limited temporal annotations is fundamental yet challenging. Existing approaches predominantly rely on topology alone, which often provides insufficient and noisy cues. This paper leverages network steady-state dynamics -- converged node states under a given dynamical process -- as an additional and widely accessible observation for network evolution history inference. We propose CS2, which explicitly models structure-state coupling to capture how topology modulates steady states and how the two signals jointly improve edge discrimination for formation-order recovery. Experiments on six real temporal networks, evaluated under multiple dynamical processes, show that CS2 consistently outperforms strong baselines, improving pairwise edge precedence accuracy by 4.0% on average and global ordering consistency (Spearman-ρ) by 7.7% on average. CS2 also more faithfully recovers macroscopic evolution trajectories such as clustering formation, degree heterogeneity, and hub growth. Moreover, a steady-state-only variant remains competitive when reliable topology is limited, highlighting steady states as an independent signal for evolution inference.