# What Do Learned Models Measure?

arXiv: https://arxiv.org/abs/2601.18278 · HTML: https://mlsanity.com/paper/2601.18278/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [The GEM Benchmark: Natural Language Generation, its Evaluation and Metrics](https://mlsanity.com/paper/2102.01672/) (2021)

## Abstract (arXiv)

In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the mapping from observations to quantities is determined implicitly by the training distribution and inductive biases, allowing multiple inequivalent mappings to satisfy standard predictive evaluation criteria. We formalize learned measurement functions as a distinct focus of evaluation and introduce measurement stability, a property capturing invariance of the measured quantity across admissible realizations of the learning process and across contexts. We show that standard evaluation criteria in machine learning, including generalization error, calibration, and robustness, do not guarantee measurement stability. Through a real-world case study, we show that models with comparable predictive performance can implement systematically inequivalent measurement functions, with distribution shift providing a concrete illustration of this failure. Taken together, our results highlight a limitation of existing evaluation frameworks in settings where learned model outputs are identified as measurements, motivating the need for an additional evaluative dimension.