"Build a wind tunnel before testing in production To prove mathematically — not just empirically — that transformers perform Bayesian updating, the speaker and his Columbia colleagues created a 'Bayesian wind tunnel': blank architectures given tasks where memorization was combinatorially impossible but the correct Bayesian posterior could be calculated analytically. The result was striking: "the transformer got the precise Bayesian posterior down to 10 to the power minus 3 bits accuracy — it was matching the distribution perfectly." The broader lesson is that when you need to rigorously validate a mechanism rather than just observe its outputs, design a controlled environment where the ground truth is known and cheating is ruled out by construction — whether in AI research, product testing, or scientific experimentation. Source: Vishal Misra, No Priors (Martin Casado), 'How LLMs Actually Work: Bayesian Inference, Causality, and the Path to AGI'"