# A Geometric Lens on Physics-Aligned Data Compression

arXiv: https://arxiv.org/abs/2606.03279 · HTML: https://mlsanity.com/paper/2606.03279/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Entroformer: A Transformer-based Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2202.05492/) (2022)
- [Video Coding for Machines: A Paradigm of Collaborative Compression and Intelligent Analytics](https://mlsanity.com/paper/2001.03569/) (2020)
- [Joint Global and Local Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/2112.04487/) (2021)
- [RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2405.12497/) (2024)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [Learned Image Compression with Dictionary-based Entropy Model](https://mlsanity.com/paper/2504.00496/) (2025)
- [Exploring Autoencoder-based Error-bounded Compression for Scientific Data](https://mlsanity.com/paper/2105.11730/) (2021)
- [A Survey on Error-Bounded Lossy Compression for Scientific Datasets](https://mlsanity.com/paper/2404.02840/) (2024)
- [A Physics-Informed Vector Quantized Autoencoder for Data Compression of Turbulent Flow](https://mlsanity.com/paper/2201.03617/) (2022)
- [NeurLZ: An Online Neural Learning-Based Method to Enhance Scientific Lossy Compression](https://mlsanity.com/paper/2409.05785/) (2024)
- [Scalable Hybrid Learning Techniques for Scientific Data Compression](https://mlsanity.com/paper/2212.10733/) (2022)
- [Image Coding for Machines via Feature-Preserving Rate-Distortion Optimization](https://mlsanity.com/paper/2504.02216/) (2025)

## Built on by (most cited first, 1 of 1)

- [Synthesizing Physics Formulae with Transformers](https://mlsanity.com/paper/2610.03947/) (2026)

## Abstract (arXiv)

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.