Data geometry preserves prediction but reshapes explanation
Abstract
Across scientific domains, empirical data often give rise to positive semidefinite matrices that encode similarities, couplings or interactions and induce natural geometries. We investigate whether changing the geometry used to compare the same empirical representations preserves subject-level performance and the local structures from which explanations are derived, a question we term the prediction explanation invariance problem. We address this problem across morphometric MRI, fMRI and EEG data by comparing Frobenius and trace geometries applied to the same empirical matrices. Predictive performance was broadly preserved across geometries, but comparable performance did not imply agreement in subject-level decision scores or predicted labels. Predictive similarity also masked geometry-dependent differences in local neighbourhoods, perturbation sensitivities and explanatory rankings. Dimensionality reduction made the two subject-space geometries progressively more concordant, while classification performance and decision-level agreement declined. These results identify data geometry as a hidden degree of freedom in explainability: similar performance does not guarantee invariant decisions or explanations.
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BibTeX
@misc{amoroso2026data,
title = {{Data geometry preserves prediction but reshapes explanation}},
author = {Nicola Amoroso and Mario Caruso and Marianna La Rocca and Loredana Bellantuono and Tommaso Maggipinto and Michele Morelli and Sabina Tangaro and Marco Tatullo and Roberto Bellotti and Ester Pantaleo and Alfonso Monaco},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08377},
eprint = {2610.08377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08377},
}
RIS
TY - UNPB
TI - Data geometry preserves prediction but reshapes explanation
AU - Nicola Amoroso
AU - Mario Caruso
AU - Marianna La Rocca
AU - Loredana Bellantuono
AU - Tommaso Maggipinto
AU - Michele Morelli
AU - Sabina Tangaro
AU - Marco Tatullo
AU - Roberto Bellotti
AU - Ester Pantaleo
AU - Alfonso Monaco
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08377
UR - https://arxiv.org/abs/2610.08377
AB - Across scientific domains, empirical data often give rise to positive semidefinite matrices that encode similarities, couplings or interactions and induce natural geometries. We investigate whether changing the geometry used to compare the same empirical representations preserves subject-level performance and the local structures from which explanations are derived, a question we term the prediction explanation invariance problem. We address this problem across morphometric MRI, fMRI and EEG data by comparing Frobenius and trace geometries applied to the same empirical matrices. Predictive performance was broadly preserved across geometries, but comparable performance did not imply agreement in subject-level decision scores or predicted labels. Predictive similarity also masked geometry-dependent differences in local neighbourhoods, perturbation sensitivities and explanatory rankings. Dimensionality reduction made the two subject-space geometries progressively more concordant, while classification performance and decision-level agreement declined. These results identify data geometry as a hidden degree of freedom in explainability: similar performance does not guarantee invariant decisions or explanations.
ER -