# The Graph-Embedded Hazard Model (GEHM): Stochastic Network Survival Dynamics on Economic Graphs

arXiv: https://arxiv.org/abs/2512.14705 · HTML: https://mlsanity.com/paper/2512.14705/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Optimal Survival Trees](https://mlsanity.com/paper/2012.04284/) (2020)
- [Dynamic Portfolio Rebalancing: A Hybrid new Model Using GNNs and Pathfinding for Cost Efficiency](https://mlsanity.com/paper/2410.01864/) (2024)
- [Detecting Financial Fraud with Hybrid Deep Learning: A Mix-of-Experts Approach to Sequential and Anomalous Patterns](https://mlsanity.com/paper/2504.03750/) (2025)

## Abstract (arXiv)

This paper develops a nonlinear evolution framework for modelling survival dynamics on weighted economic networks by coupling a graph-based p-Laplacian diffusion operator with a stochastic structural drift. The resulting finite-dimensional PDE--SDE system captures how node-level survival reacts to nonlinear diffusion pressures while an aggregate complexity factor evolves according to an Ito process. Using accretive operator theory, nonlinear semigroup methods, and stochastic analysis, we establish existence and uniqueness of mild solutions, derive topology-dependent energy dissipation inequalities, and characterise the stability threshold separating dissipative, critical, amplifying, and explosive regimes. Numerical experiments on Barab'asi--Albert networks confirm that hub dominance magnifies nonlinear gradients and compresses stability margins, producing heavy-tailed survival distributions and occasional explosive behaviour.