Title: A Geometric Perspective on Physics-Aligned Data Compression

Abstract

While physics-informed loss functions are becoming a standard tool for training learned compressors in AI for Science, their specific effects on rate-distortion performance are not yet well characterized. Typically, at a fixed bitrate, these objectives succeed in maintaining the integrity of specific physical observables but often do so at the expense of overall reconstruction fidelity. This study presents a local geometric framework to explain this tradeoff, revealing that it is driven by the interplay between latent-space sensitivities arising from the entropy model, the physical observable, and the distortion metric. These interactions create preferred directions at each operating point, dictating where compression noise must be minimized and resulting in an anisotropic error-allocation strategy. When these directional preferences are misaligned, enhancing the physical observable at a constant rate inevitably degrades standard distortion, thereby setting a fundamental boundary on simultaneous preservation. We formalize this phenomenon via a local tangent-space rate-distortion law and propose a practical alignment diagnostic rooted in the overlap of dominant eigenspaces. Experimental results across various scientific fields substantiate the theory, demonstrating that the proposed diagnostic effectively correlates with the observed trade-offs in both data and physics spaces.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC