# Generalization bounds and sample complexity for remaining useful life prediction from complete degradation trajectories

arXiv: https://arxiv.org/abs/2607.23454 · HTML: https://mlsanity.com/paper/2607.23454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 59 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)
- [Dual Aspect Self-Attention based on Transformer for Remaining Useful Life Prediction](https://mlsanity.com/paper/2106.15842/) (2021)
- [ChatGPT-Like Large-Scale Foundation Models for Prognostics and Health Management: A Survey and Roadmaps](https://mlsanity.com/paper/2305.06472/) (2023)
- [Deep Domain Adaptation for Turbofan Engine Remaining Useful Life Prediction: Methodologies, Evaluation and Future Trends](https://mlsanity.com/paper/2510.03604/) (2025)

## Abstract (arXiv)

Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as O(B2√p/n), where p is the model complexity and n the number of trajectories, and a minimax lower bound proves that the Theta(p/n) rate is unimprovable. revSecond, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal O(p/n) rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias-variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class. Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. revCross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2-3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.