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.

翻译：设$A$和$B$为集合且$A \subset B$，泛化可理解为从$A$推断出足以构造$B$的假说。从$A$可推导出任意数量的假说，但其中仅有部分能泛化至$B$。如何判断哪些假说可能具有泛化能力？一种策略是选择最短的假说，将信息压缩能力等同于泛化能力（作为智能的代理指标）。我们在具身认知的数学形式化框架中对此进行检验，表明压缩既非最大化性能（以假说泛化概率衡量）的必要条件也非充分条件。我们提出一种与长度或简洁性无关的代理指标——弱度（weakness）。研究表明，若任务均匀分布，则不存在任何代理指标能在所有任务中至少达到弱度最大化的性能，同时又在至少一个任务中严格优于弱度最大化。在二进制算术任务中，比较最大化弱度与最小描述长度的实验表明，前者的泛化率是后者的1.1至5倍。我们论证这揭示了弱度是远更优的代理指标，并解释了DeepMind的统觉引擎（Apperception Engine）为何能有效实现泛化。