# Self-Organizing Survival Manifolds: A Theory for Unsupervised Discovery of Prognostic Structures in Biological Systems

arXiv: https://arxiv.org/abs/2508.06539 · HTML: https://mlsanity.com/paper/2508.06539/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 7 of 7)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics](https://mlsanity.com/paper/2505.19171/) (2025)
- [Energentic Intelligence: From Self-Sustaining Systems to Enduring Artificial Life](https://mlsanity.com/paper/2506.04916/) (2025)
- [OmicsCL: Unsupervised Contrastive Learning for Cancer Subtype Discovery and Survival Stratification](https://mlsanity.com/paper/2505.00650/) (2025)
- [Comprehensive Benchmarking of Machine Learning Methods for Risk Prediction Modelling from Large-Scale Survival Data: A UK Biobank Study](https://mlsanity.com/paper/2503.08870/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Persona-Based Evaluation Framework for Pluralistic Alignment in Generative AI](https://mlsanity.com/paper/2605.31021/) (2026)

## Abstract (arXiv)

Survival is traditionally modeled as a supervised learning task, reliant on curated outcome labels and fixed covariates. This work rejects that premise. It proposes that survival is not an externally annotated target but a geometric consequence: an emergent property of the curvature and flow inherent in biological state space. We develop a theory of Self-Organizing Survival Manifolds (SOSM), in which survival-relevant dynamics arise from low-curvature geodesic flows on latent manifolds shaped by internal biological constraints. A survival energy functional based on geodesic curvature minimization is introduced and shown to induce structures where prognosis aligns with geometric flow stability. We derive discrete and continuous formulations of the objective and prove theoretical results demonstrating the emergence and convergence of survival-aligned trajectories under biologically plausible conditions. The framework draws connections to thermodynamic efficiency, entropy flow, Ricci curvature, and optimal transport, grounding survival modeling in physical law. Health, disease, aging, and death are reframed as geometric phase transitions in the manifold's structure. This theory offers a universal, label-free foundation for modeling survival as a property of form, not annotation-bridging machine learning, biophysics, and the geometry of life itself.