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Compression is prediction
Modern language models and data compressors rely on the same fundamental principle: the better you can predict the next token, the more efficiently you can compress information.
What: The article explains how Shannon entropy, arithmetic coding, and LLM next-token prediction share a mathematical foundation, where compression is essentially a measure of how well a model can predict incoming data sequences.
Why it matters: Understanding compression helps demystify how LLMs function; a model’s training objective is to minimize cross-entropy, which is equivalent to finding the most efficient way to 'compress' the patterns of human language.
Deep dive
- Lossless compression relies on three components: transforms, models, and entropy coders.
- Entropy coders like arithmetic coding translate probability distributions into compressed bitstreams.
- Entropy is the theoretical floor of how much data can be compressed without loss.
- Using context (order-N models) significantly improves probability estimation, leading to better compression ratios.
- LLMs function as high-performance predictors that can be used for compression, though they are often computationally impractical compared to traditional algorithms like gzip or Brotli.
- Minimizing cross-entropy in LLMs is mathematically identical to building an optimal compressor.
Decoder
- Entropy: A measure of randomness or uncertainty; in information theory, it defines the minimum number of bits needed to represent data.
- Arithmetic coding: A compression method that encodes an entire input stream as a single fractional number between 0 and 1.
- Entropy coder: A component of a compression system that maps probabilities to a bitstream.
- Tokens: Atomic units of text (words or sub-words) used by LLMs for processing.
Original article
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