Hierarchical Solomonoff Induction: An Unbounded Machine Learning Model
Solomonoff Induction, or SolInd, provides an ideal unbounded model of a priori sequence prediction but cannot naturally describe extrapolation from a given training dataset, as performed by Large Language Models. We apply de Finetti's theorem on exchangeable distributions to SolInd to produce what we call Hierarchical Solomonoff Induction, or HSI, which maintains a hyperprior over all Solomonoff priors that can be conditioned on previously observed sequences. We extend Wood et al.'s proof that universal mixtures of semimeasures are equivalent to SolInd to show that universal mixtures of these mixtures are also equivalent, proving that HSI=SolInd. We also prove that HSI's excess error on a...
| Authors | Nathan Young |
|---|---|
| Primary category | cs.LG |
| Published | 2 August 2026 |
| Last updated at source | 2 August 2026 |
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