# Certified Learning under Distribution Shift: Sound Verification and Identifiable Structure

arXiv: https://arxiv.org/abs/2602.17699 · HTML: https://mlsanity.com/paper/2602.17699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)](https://mlsanity.com/paper/2301.05815/) (2023)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)
- [Prove Symbolic Regression is NP-hard by Symbol Graph](https://mlsanity.com/paper/2404.13820/) (2024)

## Abstract (arXiv)

Proposition. Let f be a predictor trained on a distribution P and evaluated on a shifted distribution Q. Under verifiable regularity and complexity constraints, the excess risk under shift admits an explicit upper bound determined by a computable shift metric and model parameters. We develop a unified framework in which (i) risk under distribution shift is certified by explicit inequalities, (ii) verification of learned models is sound for nontrivial sizes, and (iii) interpretability is enforced through identifiability conditions rather than post hoc explanations. All claims are stated with explicit assumptions. Failure modes are isolated. Non-certifiable regimes are characterized.