A mathematically optimal (but incomputable) framework for sequence prediction that formalizes Occam’s razor.
Serves as a “gold standard” for inductive reasoning and Artificial General Intelligence (AGI).
The theory uses algorithmic probability to predict the next bit in a sequence by considering every possible computer program that could have generated the data seen so far.
Core Mechanism
Assigns a “prior” probability to every hypothesis (represented as a computer program). Shorter programs are assigned higher probabilities, mathematically encoding the principle that simpler explanations are more likely to be true.
As new data arrives, the inductor uses Bayes’ rule to update these probabilities. Programs that do not produce the observed sequence are eliminated, while the remaining ones are re-weighted.
Solomonoff’s Completeness Theorem proves that this method will eventually learn to predict any computable sequence with the absolute minimum amount of error.
Despite its perfection in principle, Solomonoff induction is uncomputable.
- Infinite Resources: Calculating the universal prior requires running an infinite number of programs on a Universal Turing Machine, many of which may never halt (The Halting Problem).
- Approximations: Because it cannot be run directly, researchers use bounded approximations. Recent studies suggest that Transformer models (basis for LLMS) may be acting as practical, limited-memory approximations of Solomonoff induction.