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This research establishes a fundamental geometric limit in physics-informed data compression, demonstrating that optimizing for specific physical observables often inherently degrades standard reconstruction fidelity. By formalizing this trade-off through a local tangent-space rate-distortion law, the authors provide a diagnostic tool to align latent-space sensitivities and manage anisotropic error allocation. For practitioners in AI for Science, this work offers a critical framework for understanding and mitigating the inevitable conflicts between domain-specific accuracy and general data fidelity.
A Geometric Lens on Physics-Aligned Data Compression
arXiv:2606.03279v1 Announce Type: new Abstract: In AI for Science, physics-informed losses are increasingly used to train learned compressors for scientific data, but their rate-distortion implications remain poorly understood. At fixed bitrate, these objectives often improve preservation of a target physical observable while degrading standard reconstruction fidelity. We develop a local geometric theory showing that this tradeoff is governed by the interaction of latent-space sensitivities induced by the entropy model, the physical observable, and the distortion metric. At each operating point, these induce preferred directions along which compression noise should be suppressed, yielding an anisotropic error-allocation mechanism. When these directions are misaligned, improving the observable at fixed rate necessarily worsens standard distortion, establishing a fundamental limit on simultaneous preservation. We formalise this through a local tangent-space rate-distortion law and introduce a practical alignment diagnostic based on dominant eigenspace overlap. Experiments across scientific domains test the theory and validate that the alignment diagnostic correlates with observed data- and physics-space trade-offs.
Abstract:In AI for Science, physics-informed losses are increasingly used to train learned compressors for scientific data, but their rate-distortion implications remain poorly understood. At fixed bitrate, these objectives often improve preservation of a target physical observable while degrading standard reconstruction fidelity. We develop a local geometric theory showing that this tradeoff is governed by the interaction of latent-space sensitivities induced by the entropy model, the physical observable, and the distortion metric. At each operating point, these induce preferred directions along which compression noise should be suppressed, yielding an anisotropic error-allocation mechanism. When these directions are misaligned, improving the observable at fixed rate necessarily worsens standard distortion, establishing a fundamental limit on simultaneous preservation. We formalise this through a local tangent-space rate-distortion law and introduce a practical alignment diagnostic based on dominant eigenspace overlap. Experiments across scientific domains test the theory and validate that the alignment diagnostic correlates with observed data- and physics-space trade-offs.
Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026
Machine Learning (cs.LG)
arXiv:2606.03279 [cs.LG]
(or arXiv:2606.03279v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.03279 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026
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Full text under the publisher's open licence · 277 words