HSI, a hyperprior over all Solomonoff priors, is shown equivalent to Solomonoff Induction while enabling dataset-conditioned prediction and a training-set error bound.
Transformers As Approximations of Solomonoff Induction
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abstract
Solomonoff Induction is an optimal-in-the-limit unbounded algorithm for sequence prediction, representing a Bayesian mixture of every computable probability distribution and performing close to optimally in predicting any computable sequence. Being an optimal form of computational sequence prediction, it seems plausible that it may be used as a model against which other methods of sequence prediction might be compared. We put forth and explore the hypothesis that Transformer models - the basis of Large Language Models - approximate Solomonoff Induction better than any other extant sequence prediction method. We explore evidence for and against this hypothesis, give alternate hypotheses that take this evidence into account, and outline next steps for modelling Transformers and other kinds of AI in this way.
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cs.LG 1years
2026 1verdicts
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Hierarchical Solomonoff Induction: An Unbounded Machine Learning Model
HSI, a hyperprior over all Solomonoff priors, is shown equivalent to Solomonoff Induction while enabling dataset-conditioned prediction and a training-set error bound.