Physical Theories of Intelligence and Recursive Self-Modification

This project investigates the physical realisation of intelligence, with a particular focus on recursive self-modification as a defining characteristic of advanced intelligent systems.

Most theories of intelligence are formulated at an algorithmic or computational level, while remaining largely agnostic as to the physical conditions required for their implementation. This project asks the complementary question: under what physical theories, scales, and substrates can recursively self-modifying intelligence exist?

Possible directions include:

• the relationship between physical theories and theories of intelligence;
• recursive self-modification across different physical substrates (e.g. electronic circuits, classical computation, quantum systems, biological systems, or alternative physical realisations);
• physical and thermodynamic constraints on adaptive intelligent systems; energy efficiency, information processing, and self-improvement;
• implications for AGI architectures, controllability, and alignment;
• mathematical and computational models of adaptive self-modification;
• empirical investigation of recursive self-improvement through simulation and prototype implementations.

The precise direction will be refined according to the interests and background of participants. The overall objective is to produce publishable research suitable for submission to leading venues in artificial intelligence, machine intelligence, computational physics, or physical information processing.

The project will follow a research-oriented workflow typical of an academic laboratory, including:

• comprehensive review of the relevant literature and identification of open research questions;
• development of mathematical models and theoretical frameworks;
• rapid design and implementation of computational experiments;
• critical evaluation of experimental results;
• iterative refinement of hypotheses and manuscript preparation.

Participants are encouraged to make extensive use of modern AI systems to assist with coding, experimentation, literature exploration, and research design. However, the emphasis will remain on developing independent research capability. In particular, participants should expect to perform the core scientific reasoning, mathematical development, and manuscript writing themselves.

Recursive self-modification is widely regarded as a defining capability of advanced AI systems, yet work remains to be done to examine the physical conditions under which it is possible. Understanding the physical constraints governing adaptive self-modification, including how they differ across physical substrates and theories of computation, is important for AI safety and alignment, as it helps identify both the capabilities and fundamental limitations of increasingly autonomous systems. By clarifying when, how, and to what extent recursive self-improvement can occur, this project aims to provide a stronger scientific foundation for forecasting AI development, designing safer architectures, and developing effective control and alignment strategies. Related work includes my research on Watts per Intelligence, Quantum AIXI, and Hamiltonian Formalisms for Comparing Quantum and Classical Intelligence. Further publications are available at https://scholar.google.com/citations?user=ImlF7PsAAAAJ&hl=en.

Mentees will participate as junior researchers in an academic research project rather than as students in a taught course. The project will be collaborative, but participants will be expected to work independently between meetings, taking ownership of literature review, mathematical development, coding, experimentation, and scientific writing.

The project will begin with a structured review of the literature to identify the state of the art, competing theories, and open research questions. This should be between 20-30 pages or so (you can use LLMs but I expect you to really grasp and explain to me the state of the art). Participants will then progressively develop theoretical models, implement computational experiments, critically analyse results, and contribute to the preparation of a publication-quality manuscript. Practically this means spinning up a couple of proposals and running them by me so we can discuss objectives, research/experimental design (what we measure, how we measure it etc).

Meetings will focus on discussing research progress, evaluating ideas, troubleshooting technical issues, and refining research direction. Mentees should expect to present their work regularly and defend their reasoning, much as they would in a university research group or laboratory. Use of AI systems for literature exploration, coding, and experimentation is permitted. However, the objective is to develop strong independent research skills, so participants should expect to perform the core scientific reasoning, mathematical analysis, and manuscript writing themselves.

The ideal outcome is a research paper suitable for submission to a leading venue in artificial intelligence, machine learning, or physical information processing.

Applicants should have a strong interest in artificial intelligence, physics, control theory, or the mathematical foundations of intelligent systems. In general mentees should focus on understanding that there are various theories of intelligence (in AI and other domains) and also physical theories (which may include information-theoretic framing) and then thinking about how they relate.

The following experience would be beneficial (but not all are required):

• Comfortable reading and discussing technical research papers.
• Familiarity with linear algebra, calculus, probability, or discrete mathematics.
• Basic programming ability (preferably Python) - and even better is a rigorous capability to use AI coding agents.
• Interest in AI, machine learning, physics, information theory, or theoretical computer science.
• Willingness to independently learn unfamiliar material and engage with challenging interdisciplinary problems.
• Strong written communication and enthusiasm for research.

Prior research experience is advantageous but not required. Motivation, curiosity, and the ability to think critically are more important than specific prior knowledge.

I'm available between 6am and 11pm Australian Eastern Standard Time at the moment