Neural Diffusion Processes for Physically Interpretable Survival Prediction

2025-10-01

AI Summary

To address the challenge of achieving both physical interpretability and non-proportional hazards modeling in survival analysis, this paper proposes DeepFHT—a novel framework integrating first-hitting-time (FHT) stochastic processes with deep neural networks. DeepFHT models event times as the first passage time of a latent diffusion process to an absorbing boundary; neural networks dynamically map input features to the initial state, drift, and diffusion coefficients, thereby explicitly characterizing time-varying hazards without assuming proportional hazards. Theoretical analysis yields closed-form expressions for the survival and hazard functions, enabling physically grounded, interpretable parameterization. Empirically, DeepFHT achieves state-of-the-art predictive accuracy on synthetic and multiple real-world datasets, while simultaneously uncovering the intrinsic mechanisms linking covariates to time-dependent risk dynamics—thus bridging deep learning with stochastic process theory for principled, interpretable survival modeling.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion process to an absorbing boundary. A neural network maps input variables to physically meaningful parameters including initial condition, drift, and diffusion, within a chosen FHT process such as Brownian motion, both with drift and driftless. This yields closed-form survival and hazard functions and captures time-varying risk without assuming proportional-hazards. We compare DeepFHT with Cox regression and other existing parametric survival models, using synthetic and real-world datasets. The method achieves predictive accuracy on par with state-of-the-art approaches, while maintaining a physics-based interpretable parameterization that elucidates the relation between input features and risk. This combination of stochastic process theory and deep learning provides a principled avenue for modeling survival phenomena in complex systems.

Problem

• Models survival time as diffusion process first hitting time
• Maps input features to interpretable physical diffusion parameters
• Achieves accurate prediction while maintaining physics-based interpretability

Innovation

• Neural network maps inputs to diffusion parameters
• Uses first hitting time distributions from stochastic processes
• Yields closed-form survival functions without proportional-hazards