Transformers As Approximations of Solomonoff Induction

TL;DR

This paper investigates whether Transformer models, the foundation of large language models, approximate Solomonoff Induction more closely than other sequence prediction methods, aiming to understand their theoretical optimality.

Contribution

The paper proposes and explores the hypothesis that Transformers approximate Solomonoff Induction better than existing methods, providing a framework for future modeling of AI.

Findings

Evidence supporting Transformers as approximations of Solomonoff Induction

Alternative hypotheses considering the evidence

Outline of future research directions

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.