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

Abstract

<p>If <em>A</em> and <em>B</em> are sets such that <em>A</em> is a subset of <em>B</em>, generalisation may be understood as the inference from <em>A</em> of a hypothesis sufficient to construct <em>B</em>. One might infer any number of hypotheses from <em>A</em>, yet only some of those may generalise to <em>B</em>. 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 <em>1.1</em> and <em>5</em> 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.</p>

On the Computation of Meaning, Language Models and Incomprehensible Horrors

“…For example it assumed a measure, "weakness", which was not well defined. However, weakness is well defined in a more recent formalism of artificial general intelligence (AGI) [9] and enactive cognition [10,11], so we will instead reformulate the theory using that formalism, extending it to account for meaningful communication. We begin with cognition formalised using tasks.…”

“…This bears out experimentally in reinforcement learning with extended environments [24]. The rational course of action is to actually have co-operative intent, assuming k can perceive o's intent correctly, and that k will reciprocate in kind 11 . Inductive inference (see appendix [1]) undertaken with co-operative intent would, if undertaken by reasonably performant organisms, ensure the organisms in a population have preferences that favour symbols that mean approximately (in a behaviourally approximate manner) similar things to all members of the population.…”

Enactivism & Objectively Optimal Super-Intelligence

“…Our purpose is to explain the aforementioned subjectivity and how it might be addressed, rather than every detail of how AIXI functions. This paper is as philosophical as it is mathematical (a companion to this paper [9] focuses on the mathematical aspects of this research). As such, the following explanation of AIXI is informal and involves some abuse of notation.…”

“…To address the former two we require a measure of performance, and an alternative proxy for intelligence. Both are addressed [13,9] by companion to this paper concerning optimal hypotheses.…”

“…Unfortunately, this claim is highly subjective, because it depends upon the choice of Universal Turing Machine (UTM) [6]. We explore this problem, and formulate an approach that combines enactive cognition [7], pancomputationalism [8] and weakness as a proxy for intelligence [9].…”