In plain words: When picking which rule to trust from examples, choose the weakest one — the least restrictive about what it allows — rather than the shortest. In binary arithmetic tests it generalized 1.1 to 5 times more often than the shortest-rule choice.
Abstract
If $A$ and $B$ are sets such that $A \subset B$, generalisation may be understood as the inference from $A$ of a hypothesis sufficient to construct $B$. One might infer any number of hypotheses from $A$, yet only some of those may generalise to $B$. How can one know which are likely to generalise? One strategy is to choose the shortest, equating the ability to compress information with the ability to generalise (a proxy for intelligence). We examine this in the context of a mathematical formalism of enactive cognition. We show that compression is neither necessary nor sufficient to maximise performance (measured in terms of the probability of a hypothesis generalising). We formulate a proxy unrelated to length or simplicity, called weakness. We show that if tasks are uniformly distributed, then there is no choice of proxy that performs at least as well as weakness maximisation in all tasks while performing strictly better in at least one. In experiments comparing maximum weakness and minimum description length in the context of binary arithmetic, the former generalised at between $1.1$ and $5$ times the rate of the latter. We argue this demonstrates that weakness is a far better proxy, and explains why Deepmind's Apperception Engine is able to generalise effectively.
Michael Timothy Bennett
arXiv:2301.12987 · cs.AI, cs.LG, math.LO · submitted Jan 30, 2023 · updated Apr 11, 2024
abstract · pdf · html · Published at the 16th Conference on Artificial General Intelligence, Stockholm, 2023