Micro-Diffusion Compression -- Binary Tree Tweedie Denoising for Online Probability Estimation

Researcher Roberto Tacconelli has introduced Midicoth, a novel lossless compression system detailed in the arXiv paper 'Micro-Diffusion Compression -- Binary Tree Tweedie Denoising for Online Probability Estimation.' The core innovation is a 'micro-diffusion denoising layer' designed to fix a fundamental flaw in adaptive statistical compressors like Prediction by Partial Matching (PPM). In these models, when a data context has only been seen a few times, a default prior dominates the prediction, creating overly flat and inaccurate probability distributions. This leads to compression inefficiency. Midicoth reframes this prior smoothing as a shrinkage process and applies a reverse denoising step to correct the predicted probabilities using empirical calibration statistics.

To make this correction practical with limited data, the method employs a clever bitwise binary tree decomposition. Instead of tackling the complex problem of calibrating a single prediction across 256 possible byte values, Midicoth breaks it down into a sequence of binary decisions. This hierarchy transforms the task into multiple, simpler binary calibration problems, enabling reliable estimation of correction terms from relatively small numbers of observations. The denoising is applied in multiple successive steps, allowing each stage to refine residual errors from the previous one.

As a final, lightweight post-processing stage, the micro-diffusion layer operates after all model predictions from other components are combined. This allows it to correct systematic biases in the final probability distribution before it's used for arithmetic coding. The complete Midicoth system is fully online and integrates five components: an adaptive PPM model, a long-range match model, a trie-based word model, a high-order context model, and the micro-diffusion denoiser applied as the final, corrective blend. This approach aims to squeeze out extra compression gains by making probability estimates more accurate, especially for rare or novel data contexts.