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

arXiv: https://arxiv.org/abs/2301.12987 · HTML: https://mlsanity.com/paper/2301.12987/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Bad Universal Priors and Notions of Optimality](https://mlsanity.com/paper/1510.04931/) (2015)
- [Symbol Emergence and The Solutions to Any Task](https://mlsanity.com/paper/2109.01281/) (2021)
- [Compression, The Fermi Paradox and Artificial Super-Intelligence](https://mlsanity.com/paper/2110.01835/) (2021)
- [Computable Artificial General Intelligence](https://mlsanity.com/paper/2205.10513/) (2022)

## Built on by (most cited first, 12 of 12)

- [Emergent Causality and the Foundation of Consciousness](https://mlsanity.com/paper/2302.03189/) (2023)
- [Computational Dualism and Objective Superintelligence](https://mlsanity.com/paper/2302.00843/) (2023)
- [On the Computation of Meaning, Language Models and Incomprehensible Horrors](https://mlsanity.com/paper/2304.12686/) (2023)
- [Is Complexity an Illusion?](https://mlsanity.com/paper/2404.07227/) (2024)
- [Are Biological Systems More Intelligent Than Artificial Intelligence?](https://mlsanity.com/paper/2405.02325/) (2024)
- [Why Is Anything Conscious?](https://mlsanity.com/paper/2409.14545/) (2024)
- [Quantum AIXI: Universal Intelligence via Quantum Information](https://mlsanity.com/paper/2505.21170/) (2025)
- [What Capable Agents Must Know: Selection Theorems for Robust Decision-Making under Uncertainty](https://mlsanity.com/paper/2603.02491/) (2026)
- [Are Flat Minima an Illusion?](https://mlsanity.com/paper/2605.05209/) (2026)
- [What the F*ck Is Artificial General Intelligence?](https://mlsanity.com/paper/2503.23923/) (2025)
- [A Mind Cannot Be Smeared Across Time](https://mlsanity.com/paper/2601.11620/) (2026)
- [Why the Third Axis Is Freedom](https://mlsanity.com/paper/2608.05423/) (2026)

## Abstract (arXiv)

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.