[2301.12987] The Optimal Choice of Hypothesis Is the Weakest, Not the Shortest

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arXiv:2301.12987 (cs)

[Submitted on 30 Jan 2023 (v1), last revised 11 Apr 2024 (this version, v4)]

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

Authors:Michael Timothy Bennett<br>View a PDF of the paper titled The Optimal Choice of Hypothesis Is the Weakest, Not the Shortest, by Michael Timothy Bennett

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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.

Comments:<br>Published at the 16th Conference on Artificial General Intelligence, Stockholm, 2023

Subjects:

Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic (math.LO)

Cite as:<br>arXiv:2301.12987 [cs.AI]

(or<br>arXiv:2301.12987v4 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2301.12987

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arXiv-issued DOI via DataCite

Journal reference:<br>Proceedings of the 16th International Conference on Artificial General Intelligence. 2023. Lecture Notes in Computer Science, vol 13921. Springer. pp. 42-51

Related DOI:

https://doi.org/10.1007/978-3-031-33469-6_5

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DOI(s) linking to related resources

Submission history<br>From: Michael Timothy Bennett [view email]<br>[v1]<br>Mon, 30 Jan 2023 15:29:40 UTC (281 KB)

[v2]<br>Mon, 6 Mar 2023 01:54:22 UTC (279 KB)

[v3]<br>Tue, 25 Apr 2023 07:23:31 UTC (58 KB)

[v4]<br>Thu, 11 Apr 2024 05:02:10 UTC (58 KB)

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