We can compress data far beyond Shannon's limits by only keeping the 'logical core' needed to re-derive the facts.
April 15, 2026
Original Paper
Semantic Rate-Distortion Theory: Deductive Compression and Closure Fidelity
arXiv · 2604.11204
The Takeaway
This new rate-distortion theory focuses on preserving 'deductive closure'—the ability to reach the same logical conclusions—rather than preserving individual symbols. It suggests we can throw away massive amounts of 'raw' data as long as we keep the 'seeds' required to re-calculate it. This is a paradigm shift for data storage and transmission: we don't need the data itself, just the logic. This could lead to a new generation of 'semantic' compression that is orders of magnitude more efficient than Zip or JPEG, particularly for large-scale knowledge bases and AI memory.
From the abstract
Shannon's rate-distortion theory treats source symbols as unstructured labels. When the source is a knowledge base equipped with a logical proof system, a natural fidelity criterion is closure fidelity: a reconstruction is acceptable if it preserves the deductive closure of the original. This paper develops a rate-distortion theory under this criterion. Central to the theory is the irredundant core-a canonical generating set extracted by a fixed-order deletion procedure, from which the full dedu