Compression is prediction

Compression reduces lossless data size by exploiting redundancy, typically through transforms, probabilistic models, and entropy coders such as arithmetic or Huffman coding, which assign fewer bits to more likely symbols. Shannon entropy defines the theoretical lower bound on the average bits required per symbol for a particular probability distribution, while adding contextual information improves predictions and can substantially reduce that bound. Language models operate through the same principle: given preceding tokens, they estimate probabilities for the next token, and a well-calibrated model could be paired with an entropy coder to compress text efficiently, with incorrect low-probability predictions costing more bits. Although LLMs can outperform simpler context models in compression ratio, their large model sizes and high computational requirements make them impractical for common applications such as web-response compression, where lightweight formats like gzip and Brotli are faster and cheaper. The shared cross-entropy objective in language-model training and entropy minimization in compression supports the view that both systems fundamentally rely on prediction.

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