The paper "Is Complexity an Illusion?" (Bennett, 2024) provides a formalism for complexity, learning, inference, and generalization, and introduces a formal definition for a "policy". This reply shows that correct policies do not exist for a simple task of supervised multi-class classification, via mathematical proof and exhaustive search. Implications of this result are discussed, as well as possible responses and amendments to the theory.

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation.

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.

Software's effect upon the world hinges upon the hardware that interprets it. This tends not to be an issue, because we standardise hardware. AI is typically conceived of as a software ``mind'' running on such interchangeable hardware. This formalises mind-body dualism, in that a software ``mind'' can be run on any number of standardised bodies. While this works well for simple applications, we argue that this approach is less than ideal for the purposes of formalising artificial general intelligence (AGI) or artificial super-intelligence (ASI). The general reinforcement learning agent AIXI is pareto optimal. However, this claim regarding AIXI's performance is highly subjective, because that performance depends upon the choice of interpreter. We examine this problem and formulate an approach based upon enactive cognition and pancomputationalism to address the issue. Weakness is a measure of plausibility, a ``proxy for intelligence'' unrelated to compression or simplicity. If hypotheses are evaluated in terms of weakness rather than length, then we are able to make objective claims regarding performance (how effectively one adapts, or ``generalises'' from limited information). Subsequently, we propose a definition of AGI which is objectively optimal given a ``vocabulary'' (body etc) in which cognition is enacted, and of ASI as that which finds the optimal vocabulary for a purpose and then constructs an AGI.

Artificial general intelligence (AGI) may herald our extinction, according to AI safety research. Yet claims regarding AGI must rely upon mathematical formalisms -- theoretical agents we may analyse or attempt to build. AIXI appears to be the only such formalism supported by proof that its behaviour is optimal, a consequence of its use of compression as a proxy for intelligence. Unfortunately, AIXI is incomputable and claims regarding its behaviour highly subjective. We argue that this is because AIXI formalises cognition as taking place in isolation from the environment in which goals are pursued (Cartesian dualism). We propose an alternative, supported by proof and experiment, which overcomes these problems. Integrating research from cognitive science with AI, we formalise an enactive model of learning and reasoning to address the problem of subjectivity. This allows us to formulate a different proxy for intelligence, called weakness, which addresses the problem of incomputability. We prove optimal behaviour is attained when weakness is maximised. This proof is supplemented by experimental results comparing weakness and description length (the closest analogue to compression possible without reintroducing subjectivity). Weakness outperforms description length, suggesting it is a better proxy. Furthermore we show that, if cognition is enactive, then minimisation of description length is neither necessary nor sufficient to attain optimal performance, undermining the notion that compression is closely related to intelligence. However, there remain open questions regarding the implementation of scale-able AGI. In the short term, these results may be best utilised to improve the performance of existing systems. For example, our results explain why Deepmind's Apperception Engine is able to generalise effectively, and how to replicate that performance by maximising weakness.