这篇把Solomonoff归纳改成能基于数据集预测，证明与原版等价且误差有界，做理论的人可以看。
论文提出分层Solomonoff归纳（HSI），将de Finetti定理应用于Solomonoff归纳（SolInd），构造覆盖所有Solomonoff先验的超先验，以支持对给定数据集的外推。作者扩展了Wood等人的证明，表明通用半测度混合的混合仍等价于SolInd，即HSI=SolInd。他们还证明，HSI在任意分布上的超额误差受该分布在超先验中复杂度的限制，类比于SolInd的预测误差受Kolmogorov复杂度限制。随着数据集增长，HSI的平均超额误差收敛到0，实现极限最优预测。
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 any distribution, compared to its true generator, is bounded by that generator's complexity in the hyperprior. This result is directly comparable to SolInd's prediction error being bounded by the Kolmogorov complexity of the sequence being predicted, and forces HSI's average excess error to converge to 0 as a dataset grows, leading to optimal prediction in the limit. We claim that HSI is an ideal unbounded model of sequence prediction given a dataset in the same way that SolInd is ideal over individual sequences.