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What Do Learned Models Measure?

Indrė Žliobaitė

TL;DR

Learned models used as measurement instruments can yield inequivalent measurements of the same quantity despite similar predictive performance. The authors formalize learned measurement functions and introduce measurement stability, an invariance requirement across admissible realizations and deployment contexts, with a formal condition $m_1(\phi_{m_1}(o), c) \approx m_2(\phi_{m_2}(o), c)$. An empirical case on temperature measurement from sensor data shows predictive equivalence can mask measurement divergence under distribution shift. The work argues for stability-aware evaluation to complement traditional generalization and calibration metrics, enabling principled use of learned models as scientific instruments.

Abstract

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.

What Do Learned Models Measure?

TL;DR

Learned models used as measurement instruments can yield inequivalent measurements of the same quantity despite similar predictive performance. The authors formalize learned measurement functions and introduce measurement stability, an invariance requirement across admissible realizations and deployment contexts, with a formal condition . An empirical case on temperature measurement from sensor data shows predictive equivalence can mask measurement divergence under distribution shift. The work argues for stability-aware evaluation to complement traditional generalization and calibration metrics, enabling principled use of learned models as scientific instruments.

Abstract

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.
Paper Structure (19 sections, 2 equations, 1 figure)

This paper contains 19 sections, 2 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Learned Measurement Functions
  4. Measurement Functions vs. Predictors
  5. Non-Uniqueness and Inductive Bias
  6. Measurement as an Evaluation Object
  7. Measurement Stability
  8. Definition of Measurement Stability
  9. Contexts and Admissible Realizations
  10. Why Standard Evaluation Criteria Are Insufficient
  11. Empirical Evidence of Failure
  12. Experimental Setup
  13. Performance under Standard Evaluation Criteria
  14. Assessing Measurement Stability
  15. Stable Predictions, Unstable Measurements
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Evaluation of predictive accuracy and measurement stability. (a) Predictive performance of Model A and Model B on training and held-out test data. MSE --- mean squared error. (b) Calibration curves under temporal distribution shift comparing nominal and empirical coverage. (c) Robustness under increasing input noise. (d) Measurement stability: prediction disagreement between two models trained on different sensor subsets as a function of true temperature.

Theorems & Definitions (2)

  • Definition 3.1: Learned Measurement Function
  • Definition 4.1: Measurement Stability