Gibbs randomness-compression proposition

תקציר מקורי באנגליתarXiv:2505.23869v5 Announce Type: replace-cross Abstract: A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a lossy compression process. In building this connection, we use a performance of a learning task as a probe of compression in iterative compress-train cycles. This can be thought as iterative coarse-graining from statistical mechanics perspective using thermodynamic efficiency as a probe. We formulate this connection via comonotonic relationship within a very small decrease in compression ratio and the performance. We have showcase the validity of this proposition with a canonical vision task in deep learning with three different model compression processes as {\it a baseline model}. We use the fol