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

• URL: http://arxiv.org/abs/2512.14705v1
• Date: Sat, 06 Dec 2025 12:22:25 GMT
• Title: The Graph-Embedded Hazard Model (GEHM): Stochastic Network Survival Dynamics on Economic Graphs
• Abstract summary: This paper develops a framework for modelling survival dynamics on weighted economic networks by coupling a graph-based $p$-Laplacian diffusion operator with a structural drift.<n>The resulting finite-dimensional PDE-SDE system captures how node-level survival reacts to nonlinear diffusion pressures while an aggregate factor evolves according to an It process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Itô{} 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 Barabási--Albert networks confirm that hub dominance magnifies nonlinear gradients and compresses stability margins, producing heavy-tailed survival distributions and occasional explosive behaviour.

Related papers

• Persistent Gaussian Perturbations Prevent Oversmoothing in Recurrent Graph Neural Networks [2.8427946758947304]
  We study a recurrent graph neural network in which independent Gaussian noise is injected after every propagation step.<n>We prove that the hidden representations form a geometrically ergodic Markov chain admitting a unique invariant probability measure.<n>Our analysis reveals persistent perturbations as a fundamentally different mechanism for combating oversmoothing.
  arXiv  Detail & Related papers  (2026-07-30T13:21:18Z)
• Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts [60.95873409673775]
  identifiability in continuous-time latent differential equation models remains largely open.<n>We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism.<n>We propose a two-stage estimator for latent disentanglement and optional graph recovery.
  arXiv  Detail & Related papers  (2026-06-26T16:18:28Z)
• Stochastic Gradient Descent in the Saddle-to-Saddle Regime of Deep Linear Networks [74.46751089984072]
  gradient descent (SGD) noise on descent in deep linear networks is poorly understood.<n>We investigate the dynamics of SGD during training of DLNs in the saddle-to-saddle regime.<n>Our results establish that SGD noise encodes information about the progression of feature learning but does not fundamentally alter the saddle-to-saddle dynamics.
  arXiv  Detail & Related papers  (2026-04-07T18:43:08Z)
• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Stochastic Deep Learning: A Probabilistic Framework for Modeling Uncertainty in Structured Temporal Data [0.0]
  I propose a novel framework that integrates differential equations (SDEs) with deep generative models to improve uncertainty in machine learning applications involving structured and temporal data.<n>This approach, termed Latent Differential Inference (SLDI), embeds an It SDE in the latent space of a variational autoencoder.<n>The drift and diffusion terms of the SDE are parameterized by neural networks, enabling data-driven inference and generalizing classical time series models to handle irregular sampling and complex dynamic structure.
  arXiv  Detail & Related papers  (2026-01-08T18:53:59Z)
• An Operator-Consistent Graph Neural Network for Learning Diffusion Dynamics on Irregular Meshes [0.0]
  Multiphysics interactions such as diffusion, damage, and healing often take place on irregular meshes.<n>We develop an operator-consistent graph neural network (OCGNN-PINN) that approximates PDE evolution under physics-informed constraints.
  arXiv  Detail & Related papers  (2025-12-05T06:58:25Z)
• A PDE Perspective on Generative Diffusion Models [8.328108675535562]
  We develop a rigorous partial differential equation (PDE) framework for score-based diffusion processes.<n>We derive sharp $Lp$-stability estimates for the associated score-based Fokker-Planck dynamics.<n>Results yield a theoretical guarantee that, under exact guidance, diffusion trajectories return to the data manifold.
  arXiv  Detail & Related papers  (2025-11-08T09:19:25Z)
• Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation [0.0]
  This paper introduces a emphstructure-preserving PINN framework for the nonlinear Korteweg--de Vries (KdV) equation.<n>The proposed method embeds the conservation of mass and Hamiltonian energy directly into the loss function.<n>We successfully reproduces hallmark behaviors of KdV dynamics while maintaining conserved invariants.
  arXiv  Detail & Related papers  (2025-11-01T06:07:24Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics.<n>We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots [12.57987355677862]
  APPEX is an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals.<n>We show that APPEX iteratively decreases Kullback-Leibler divergence to the true solution, and demonstrate its effectiveness on simulated data from linear additive noise SDEs.
  arXiv  Detail & Related papers  (2024-10-30T06:28:21Z)
• Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks [0.0]
  We extend the existing framework of inelastic artificial neural networks (iCANNs) by incorporating plasticity to increase their applicability to model more complex material behavior.<n>Our framework captures both linear and nonlinear kinematic hardening behavior.
  arXiv  Detail & Related papers  (2024-07-27T19:19:42Z)
• Optimization-Induced Graph Implicit Nonlinear Diffusion [64.39772634635273]
  We propose a new kind of graph convolution variants, called Graph Implicit Diffusion (GIND) GIND implicitly has access to infinite hops of neighbors while adaptively aggregating features with nonlinear diffusion to prevent over-smoothing. We show that the learned representation can be formalized as the minimizer of an explicit convex optimization objective.
  arXiv  Detail & Related papers  (2022-06-29T06:26:42Z)
• Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations [57.15855198512551]
  We propose a novel score-based generative model for graphs with a continuous-time framework. We show that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule.
  arXiv  Detail & Related papers  (2022-02-05T08:21:04Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• Training Deep Energy-Based Models with f-Divergence Minimization [113.97274898282343]
  Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging. We propose a general variational framework termed f-EBM to train EBMs using any desired f-divergence. Experimental results demonstrate the superiority of f-EBM over contrastive divergence, as well as the benefits of training EBMs using f-divergences other than KL.
  arXiv  Detail & Related papers  (2020-03-06T23:11:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.