Compression, The Fermi Paradox and Artificial Super-Intelligence

2023

Preprint

If A and B are sets such that A ⊂ 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 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 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.

Section: Discussionmentioning

confidence: 99%

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

2023

Preprint

Section: Discussion and Limitationsmentioning

confidence: 99%

Computable Artificial General Intelligence

2022

Preprint

Self Cite

The general reinforcement learning agent AIXI may be the only mathematical formalism of artificial general intelligence (AGI) supported by proof that its performance, measured according to a description of intelligence, is optimal. Unfortunately AIXI is incomputable, and its performance is subjective. This paper proposes an alternative, also supported by proof, which overcomes both problems. Integrating research from cognitive science (enactivism), philosophy of language (intension and extension), machine learning and planning (satplan), the notion of an arbitrary task is given mathematical rigour. This serves as an enactive, unified model of learning and reasoning within which a description of intelligence is formalised, along with a computable universal prior we prove grants optimal performance according to that description. This mathematical proof is then further supported with experimental results. The foremost limitation is that intelligence is computationally complex, and must be coupled with domain specific inductive biases to make real-world tasks of practical significance tractable (such as the domain of all tasks an average human might expect to undertake). Finally, by unifying concepts from AI, cognitive science and philosophy in one formalism, we have defined shared language to enable collaborative bridges within and beyond these fields.

“…Finally, attribution requires a measure of success. Success is determined by preferences, which must resemble human primitives of cognition (hunger, attraction etc) if an agent is to communicate and co-operate with humans [60]. The results here can also be applied to more immediate effect in the context of existing approaches to narrow AI such as neural networks, results of which are forthcoming as mentioned in section 5.2.…”

Section: Future Researchmentioning

confidence: 92%

Computable Artificial General Intelligence

2022

Preprint

Self Cite

The general reinforcement learning agent AIXI may be the only mathematical formalism of artificial general intelligence (AGI) supported by proof that its performance is optimal. This is achieved using compression as a proxy for intelligence. Unfortunately, AIXI is incomputable and claims of its optimality were later shown to be subjective. This paper proposes an alternative, supported by proof, which overcomes both problems. Integrating research from cognitive science (enactivism), philosophy (intension and extension), machine learning and planning (satplan), an arbitrary task is given mathematical rigour. This serves as an enactive model of learning and reasoning within which a description of intelligence is formalised. Instead of compression we use weakness as our proxy, and the result is both computable and objective. We formally prove that maximising weakness maximises intelligence. This proof is then further supported with experimental results comparing weakness and description length (the closest analogue to compression possible under the enactive model that would not reintroduce the problem of subjective performance). Our results show that weakness outperforms description length, and is a better proxy for intelligence. The foremost limitation is that intelligence as we have defined it is computationally complex, but may be coupled with domain specific inductive biases to make real-world domains of practical significance tractable (e.g. the domain of all tasks a human would undertake). Like AIXI this is not intended to be a panacea but to demonstrate useful principles, which may be integrated with existing tools such as neural networks to improve performance.