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      The Optimal Choice of Hypothesis Is the Weakest, Not the Shortest

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          Abstract

          If A and B are sets such that AB, 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 other words, weakness is the pareto optimal choice of proxy. 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.

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          Author and article information

          Journal
          30 January 2023
          Article
          2301.12987
          da41de08-c65b-467f-8d48-997b310ed02b

          http://creativecommons.org/licenses/by-nc-nd/4.0/

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          Custom metadata
          cs.AI cs.LG cs.SC math.LO

          Theoretical computer science,Artificial intelligence,Logic & Foundation
          Theoretical computer science, Artificial intelligence, Logic & Foundation

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