What Can Language Models Inherit from Solomonoff Induction? Limits, Attainable Properties, and What Served Conditionals Reveal
A familiar line of reasoning runs as follows: language models are flexible approximators trained under a strictly proper loss, so scale brings them closer to Solomonoff induction, and their predictive success is evidence of that approach. We apply known results from algorithmic information theory, universal prediction and Bayesian consistency. In its uniform form the conclusion holds for no computable model: each has cheap environments it never learns, and every uniformly computable family of total predictors shares one on which each member fails beyond a horizon growing with its index, so ``closer'' can hold only pointwise, one environment at a time. Nor could the offered routes certify ...
| Authors | Luan Ozelim, Abicumaran Uthamacumaran, Hector Zenil |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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