# Understanding Overparametrization in Survival Models through Interpolation

arXiv: https://arxiv.org/abs/2512.12463 · HTML: https://mlsanity.com/paper/2512.12463/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 13 Dec 2025.

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

- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Classification vs regression in overparameterized regimes: Does the loss function matter?](https://mlsanity.com/paper/2005.08054/) (2020)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [A Scalable Discrete-Time Survival Model for Neural Networks](https://mlsanity.com/paper/1805.00917/) (2018)
- [High-dimensional analysis of double descent for linear regression with random projections](https://mlsanity.com/paper/2303.01372/) (2023)
- [Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework](https://mlsanity.com/paper/1801.05512/) (2018)
- [Analytic Study of Double Descent in Binary Classification: The Impact of Loss](https://mlsanity.com/paper/2001.11572/) (2020)
- [Harmless interpolation in regression and classification with structured features](https://mlsanity.com/paper/2111.05198/) (2021)
- [Phenomenology of Double Descent in Finite-Width Neural Networks](https://mlsanity.com/paper/2203.07337/) (2022)

## Built on by (most cited first, 2 of 2)

- [Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting](https://mlsanity.com/paper/2602.05887/) (2026)
- [Non-Crossing Deep Quantile Regression for Distributional Survival Prediction](https://mlsanity.com/paper/2608.16864/) (2026)

## Abstract (arXiv)

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, double-descent, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define interpolation and finite-norm interpolation, two key characteristics of loss-based models to understand double-descent. We then show the existence (or absence) of (finite-norm) interpolation of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of interpolation and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.