While not exactly the idea in your post, this recent paper by Dubois, Bloem-Reddy, Ullrich, and Maddison on "Lossy Compression for Lossless Prediction" (https://arxiv.org/abs/2106.10800) kinda gets at this idea.

From the abstract:

Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations...

Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than 1000× on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance.

Pretty cool stuff!