Singular Learning Theory Comprehensive - 2

On LessWrong, Agastya Agrawal published the second comprehensive tutorial on Singular Learning Theory, continuing earlier foundational work. The post establishes four key definitions: realizability, regularity, essential uniqueness, and the relative variance of log density ratio functions. Agrawal then shows how generating functions reveal the connections between these concepts and Bayesian observables like free energy, loss functions, and WAIC. The material unpacks the formal relationships between a true distribution, a statistical model, and a prior—central to understanding how Bayesian learning behaves in theory. The post is technically dense, aimed at readers following Watanabe's mathematical framework, and includes notebook implementations and problem sets with solutions for those ready to work through the derivations.

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