# Detecting underdetermination in parameterized quantum circuits

arXiv: https://arxiv.org/abs/2504.03315 · HTML: https://mlsanity.com/paper/2504.03315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 55 of its 97 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 30 of 55)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
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- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Artificial Intelligence, Values and Alignment](https://mlsanity.com/paper/2001.09768/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [AI Alignment: A Comprehensive Survey](https://mlsanity.com/paper/2310.19852/) (2023)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021)
- [Secure and Robust Machine Learning for Healthcare: A Survey](https://mlsanity.com/paper/2001.08103/) (2020)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Shaping the learning landscape in neural networks around wide flat minima](https://mlsanity.com/paper/1905.07833/) (2019)
- [Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspective](https://mlsanity.com/paper/2206.12227/) (2022)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Fairness in Learning-Based Sequential Decision Algorithms: A Survey](https://mlsanity.com/paper/2001.04861/) (2020)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [Towards quantum enhanced adversarial robustness in machine learning](https://mlsanity.com/paper/2306.12688/) (2023)
- [Exponential separations between classical and quantum learners](https://mlsanity.com/paper/2306.16028/) (2023)

## Abstract (arXiv)

A central question in machine learning is how reliable the predictions of a trained model are. Reliability includes the identification of instances for which a model is likely not to be trusted based on an analysis of the learning system itself. Such unreliability for an input may arise from the model family providing a variety of hypotheses consistent with the training data, which can vastly disagree in their predictions on that particular input point. This is called the underdetermination problem, and it is important to develop methods to detect it. With the emergence of quantum machine learning (QML) as a prospective alternative to classical methods for certain learning problems, the question arises to what extent they are subject to underdetermination and whether similar techniques as those developed for classical models can be employed for its detection. In this work, we first provide an overview of concepts from Safe AI and reliability, which in particular received little attention in QML. We then explore the use of a method based on local second-order information for the detection of underdetermination in parameterized quantum circuits through numerical experiments. We further demonstrate that the approach is robust to certain levels of shot noise. Our work contributes to the body of literature on Safe Quantum AI, which is an emerging field of growing importance.