Robust Computer Algebra, Theorem Proving, and Oracle AI

TL;DR

This paper surveys the concept of oracles in superintelligent AI, focusing on computer algebra systems and theorem provers as domain-specific oracles, and discusses their potential for enhancing AI safety through provable guarantees.

Contribution

It identifies the limitations of current question-answering systems as oracles and proposes integrating computer algebra systems with theorem provers to address AI safety challenges.

Findings

Computer algebra systems are primitive domain-specific oracles for mathematics.

Integrating CASs with theorem provers presents concrete research challenges.

Architectural deficiencies in CASs impact their use as safe oracles.

Abstract

In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.