Transformers As Approximations of Solomonoff Induction
This addresses the theoretical foundation of AI sequence prediction, potentially linking practical models to optimal limits, but it is incremental as it explores a hypothesis without new empirical results.
The paper investigates whether Transformer models approximate Solomonoff Induction, an optimal sequence prediction algorithm, better than other existing methods, by exploring evidence and proposing alternative hypotheses.
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.