# Loss Invariance Determines What Concept Layers Encode: Volume Grounding in Echocardiography

arXiv: https://arxiv.org/abs/2607.25748 · HTML: https://mlsanity.com/paper/2607.25748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Do Concept Bottleneck Models Learn as Intended?](https://mlsanity.com/paper/2105.04289/) (2021)
- [Incremental Residual Concept Bottleneck Models](https://mlsanity.com/paper/2404.08978/) (2024)
- [Towards Robust Metrics for Concept Representation Evaluation](https://mlsanity.com/paper/2301.10367/) (2023)
- [On the Concept Trustworthiness in Concept Bottleneck Models](https://mlsanity.com/paper/2403.14349/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [There Was Never a Bottleneck in Concept Bottleneck Models](https://mlsanity.com/paper/2506.04877/) (2025)
- [Symbol Grounding in Neuro-Symbolic AI: A Gentle Introduction to Reasoning Shortcuts](https://mlsanity.com/paper/2510.14538/) (2025)
- [Learning a Clinically-Relevant Concept Bottleneck for Lesion Detection in Breast Ultrasound](https://mlsanity.com/paper/2407.00267/) (2024)
- [Ablation-Corrected Evaluation of Attribution Maps in Echocardiographic Ejection-Fraction Models](https://mlsanity.com/paper/2607.13738/) (2026)
- [Spatially Grounded Concept Bottleneck Models for Trustworthy Breast Ultrasound Diagnosis](https://mlsanity.com/paper/2607.20691/) (2026)

## Abstract (arXiv)

Objective: Concept bottleneck models route prediction through interpretable intermediate variables, and their validity is normally judged by how accurately those variables are predicted. We ask whether that judgement is sufficient, using left ventricular volumes as the concepts underlying ejection fraction estimation from echocardiographic video. Methods: A video transformer encoder was trained on a publicly available echocardiography dataset. End-systolic and end-diastolic volumes formed a concept layer from which ejection fraction was computed analytically, with no residual path to the output. We compared training under an ejection fraction objective alone against training with additional supervision of the volumes in millilitres, and evaluated both on 1276 held-out studies. Results: The concept bottleneck did not increase ejection fraction error relative to direct regression, at 6.89 against 7.13 mean absolute error. Without volume supervision, however, the spread of predicted volumes collapsed to 0.1 millilitres against reference spreads of 35.7 and 45.7 millilitres, while correlation was partly preserved. We show that this follows from an invariance property of the objective: ejection fraction is a ratio and is unchanged when both volumes are rescaled, so the loss determines the concept layer only up to scale. Supervision in absolute units reduced volume error from 89.8 to 25.8 millilitres at a cost of 0.4 in ejection fraction error. Conclusion: Concept accuracy alone can conceal a concept layer that carries no physical scale. Significance: Interpretable intermediate variables in clinical models should be validated against the invariance structure of the training objective, not only against prediction accuracy.