Learning Criticality: Statistical Limits of Predicting Phase Transitions in Random Networks

TMLR Paper5067 Authors

Abstract: We study the fundamental limits of learning phase transitions in random graph models from observational data. Motivated by applications in infrastructure resilience, epidemics, and complex systems, we ask: when can a machine learning algorithm predict the onset of a critical transition (e.g., percolation, connectivity collapse, synchronization breakdown) purely from sampled system trajectories? We introduce a formal framework that connects the statistical learnability of phase transitions to large deviations, generalization bounds, and graph ensemble parameters. We prove that for certain classes of random graphs (e.g., Erdős–Rényi, configuration models), there exists a universal scaling law that governs the sample complexity required to distinguish subcritical from supercritical regimes. Moreover, we identify regimes where no learning algorithm—regardless of architecture—can outperform random guessing, due to vanishing information gain near the critical point. Our results establish a phase diagram of learnability and provide a theoretical foundation for predictive algorithms in networked stochastic systems near criticality.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=jdBD9ZiuuB&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

Changes Since Last Submission:

This is a corrected resubmission of the manuscript that was previously desk-rejected on June 9, 2025, due to formatting issues (specifically, incorrect font not compliant with the TMLR style guide).

In this version, we have:
- Used the official TMLR LaTeX style file with no modifications,
- Ensured correct use of 10pt Computer Modern font throughout,
- Removed all custom spacing or font overrides.

No changes have been made to the technical content of the paper. The submission now fully conforms to TMLR's style and formatting requirements.

Assigned Action Editor: ~Jean_Barbier2

Submission Number: 5067