Every sentence has a unique address in a probability universe, a number line from 0 to 1. GPT maps texts to these addresses, compressing them into compact codes. How does this cosmic navigation work, and why is it a breakthrough for compression?
Mapping Sentences to Intervals
Each sequence corresponds to a unique interval in [0, 1), with its length equaling the sequence’s probability. For “cat eats fish” (P(“cat”)=0.5, P(“eats” | “cat”)=0.7, P(“fish” | “cat eats”)=0.4), the interval is [0, 0.14), with length 0.5 * 0.7 * 0.4 = 0.14. Arithmetic coding narrows this interval step-by-step, outputting a binary number. Decompression retraces the path, ensuring perfection. Why are these intervals unique?
The Power of Information Theory
The interval’s length reflects the sequence’s probability, with high-probability sequences needing fewer bits (-log₂(0.14) ≈ 2.84 bits). This approaches Shannon’s entropy limit, where GPT’s precise predictions minimize bits for semantic data. Why does predictability reduce bit requirements?
Why It’s Revolutionary
Unlike traditional methods (e.g., Huffman coding), GPT’s approach handles continuous streams and leverages semantic patterns, making it ideal for texts. What data types might benefit most, and how could this evolve with better models?
Original post: https://liweinlp.com/13275
