Project details
Overview
We will formalise and prove properties of scale-free systems that involve AI. We aim to develop tools that can be applied to current (e.g. language model agents (LMAs)) and future systems. To achieve our goals we aim to formally unify and build upon two lines of research:
• Scale-free systems within Pancomputational Enactivism: Combining Pancomputational Enactivism [1, 2] with biological and complex systems results [3–9], we have formalised adaptation at different scales and levels of abstraction and distribution [10]. This theory rigorously compares systems by how they delegate control. It has provided a variety of formal proofs, including an objective upper bound on intelligence [2? ] (in response to AIXI’s subjectivity pointed out by Leike and Hutter [11]). It shows the scale-free, distributed, bottom-up architecture of biological self-organisation allows for more efficient adaptation than the static top-down architecture typical of computers. Artificial intelligence rests on a static, human-engineered ‘stack’, and only adapts at high levels of abstraction. Scale free, decentralised systems are more ‘intelligent’ because they must delegate adaptation down the stack, to lower levels of abstraction. This research shows how a failure state analogous to cancer [9, 12] when control is insufficiently delegated in a distributed system under adverse conditions. This is highly relevant to AI safety and alignment of multi-agent systems and distributed superintelligence. It establishes a precondition for alignment.
• Mathematical foundations for measuring agency: This project led by Perrier [13, 14] provides mathematical tools which measure critical ontological properties of language model agents (LMA) [15–27]: how persistent agentic identity is over time (diachronic identity) or how identity persists across distributed networks and scaffolding (sycnhronic identity). Our framework quantifies the stability of an LMA’s agentic identity, so that they can be aligned top-down with a particular purpose. This is so we can ensure an LMA remains within rigorously defined safe boundaries as it interact with uncertain, real-world environments. We aim to apply techniques from geometric control theory (in which Perrier has particular expertise) to model control of AI agents. For example, we explore modelling agentic behaviour as paths across suitably parameterised manifolds. This will let us assess the extent to which analytic methods (e.g. optimal path theory) can be used in concert with control to provide guaranteed agentic trajectories within provable bounds. We have already been collaborating on papers and experiments and have made some progress.
The former exames alignment bottom up, while the latter measures it top-down. Unifying these results is a path towards practical verification methods for alignment in the context of scale-free systems. We plan to run experiments and write several papers, delivering practical open source tools that can be applied immediately to LMAs and longer term to distributed intelligent systems of ASL-4 and higher [28]. This integrated approach challenges current assumptions and opens new research paths for alignment.
Plan
We will construct a common mathematical language that bridges the gap between the bottom-up, multilayer architecture and the top-down safety guarantees. Then we will work on theorems and proofs that guarantee the safety and integrity of scale free systems both top-down and bottom-up. Once the theoretical foundations are established, we will develop a framework to evaluate LMAs and run experiments to test our results in representative scenarios, ensuring that the mathematical safety properties hold in practice. The expected outcome is tools and experimental results that validate our formal results, demonstrating that AI systems designed with our framework operate safely even under adverse or unexpected conditions. Our research will involve collaboration with experts in complex systems, biology, and AI. This collaborative effort will ensure that our mathematical abstractions are both theoretically sound and practically relevant. The expected outcome is refined models and proofs that incorporate diverse perspectives and address the challenges of real-world deployment. To reiterate:
• O1 - Formal Foundations: We aim to formally merge the aforementioned lines of research. This will give us a versatile foundation on which to build.
• O2 - Proofs: We will then develop a rigorous, modular framework with formal proofs and methods to to verify safety constraints in distributed, multi-layered, scale-free systems that involve AI.
• O3 - Application: We aim to produce practical tools, and test them against current LMA and simulated scale-free systems that are likely to exist in future.
References
[1] Bennett, M.T.: Computational dualism and objective superintelligence. In: 17th International Conference on Artificial General Intelligence. Springer (2024)
[2] Bennett, M.T.: The optimal choice of hypothesis is the weakest, not the shortest. In: 16th International Conference on Artificial General Intelligence, pp. 42–51. Springer (2023)
[3] Friston, K.J., Heins, C., Verbelen, T., Costa, L.D., Salvatori, T., Markovic, D., Tschantz, A., Koudahl, M.T., Buckley, C.L., Parr, T.: From pixels to planning: scale-free active inference. CoRR abs/2407.20292 (2024)
[4] Sol´e, R., Seoane, L.F.: Evolution of brains and computers: The roads not taken. Entropy 24(5), 665 (2022)
[5] Sol´e, R., Kempes, C.P., Corominas-Murtra, B., De Domenico, M., Kolchinsky, A., Lachmann, M., Libby, E., Saavedra, S., Smith, E., Wolpert, D.: Fundamental constraints to the logic of living systems. Interface Focus 14(5), 20240010 (2024)
[6] Man, K., Damasio, A.R.: Homeostasis and soft robotics in the design of feeling machines. Nature Machine Intelligence 1, 446–452 (2019)
[7] Ororbia, A., Friston, K.: Mortal Computation: A Foundation for Biomimetic Intelligence (2024). https://arxiv.org/abs/2311.09589
[8] McMillen, P., Levin, M.: Collective intelligence: A unifying concept for integrating biology across scales and substrates. Communications Biology 7(1), 378 (2024)
[9] Levin, M.: Bioelectrical approaches to cancer as a problem of the scaling of the cellular self. Progress in Biophysics and Molecular Biology 165, 102–113 (2021). Cancer and Evolution
[10] Bennett, M.T.: Are biological systems more ‘intelligent’ than artificial intelligence? (2025)
[11] Leike, J., Hutter, M.: Bad universal priors and notions of optimality. Proceedings of The 28th COLT, PMLR, 1244–1259 (2015)
[12] Davies, P.C.W., Lineweaver, C.H.: Cancer tumors as metazoa 1.0: tapping genes of ancient ancestors. Physical Biology 8(1) (2011)
[13] Elija Perrier, M.T.B.: Position: Stop acting like language model agents are normal agents (2025)
[14] Elija Perrier, M.T.B.: Measuring agency of language model agents (2025)
[15] Maes, P.: Agents that reduce work and information overload. Communications of the ACM 37(7), 30–40 (1994) https://doi.org/10.1145/176789.176792 . Accessed 2024-06-17
[16] Maes, P.: Artificial life meets entertainment: lifelike autonomous agents. Communications of the ACM 38(11), 108–114 (1995)
[17] Lieberman, H.: Autonomous interface agents. In: Proceedings of the ACM SIGCHI Conference on Human Factors in Computing systems. CHI ’97, pp. 67–74. Association for Computing Machinery, New York, NY, USA (1997).
[18] Jennings, N.R., Sycara, K., Wooldridge, M.: A roadmap of agent research and development. Autonomous agents and multi-agent systems 1, 7–38 (1998). Springer
[19] Johnson, D.G.: Software Agents, Anticipatory Ethics, and Accountability. In: Marchant, G.E., Allenby, B.R., Herkert, J.R. (eds.) The Growing Gap Between Emerging Technologies and Legal-Ethical Oversight: The Pacing Problem, pp. 61–76. Springer, Dordrecht (2011).
[20] Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. The MIT Press, Cambridge, Massachusetts (2018).
[21] Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 4th edn. (2021)
[22] Chan, A., Salganik, R., Markelius, A., Pang, C., Rajkumar, N., Krasheninnikov, D., Langosco, L., He, Z., Duan, Y., Carroll, M., Lin, M., Mayhew, A., Collins, K., Molamohammadi, M., Burden, J., Zhao, W., Rismani, S., Voudouris, K.,
Bhatt, U., Weller, A., Krueger, D., Maharaj, T.: Harms from Increasingly Agentic Algorithmic Systems. In: Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency. FAccT ’23, pp. 651–666. Association for Computing Machinery, New York, NY, USA (2023).
[23] Wu, Q., Bansal, G., Zhang, J., Wu, Y., Li, B., Zhu, E., Jiang, L., Zhang, X., Zhang, S., Liu, J., Awadallah, A.H., White, R.W., Burger, D., Wang, C.: AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation Framework. (2023).
[24] OpenAI: OpenAI Charter (2018). https://openai.com/charter/
[25] Gabriel, I. et. al.: The Ethics of Advanced AI Assistants. arXiv. arXiv:2404.16244 [cs] (2024). http://arxiv.org/abs/2404.16244 Accessed 2024-04-26
[26] Kolt, N.: Governing AI Agents, Rochester, NY (2024).
[27] Lazar, S.: Frontier AI Ethics: Anticipating and Evaluating the Societal Impacts of Generative Agents. arXiv. arXiv:2404.06750 [cs] (2024).
[28] Anthropic: Anthropic’s responsible scaling policy (2023).
[29] Fields, C., Levin, M.: Scale-free biology: Integrating evolutionary and developmental thinking. BioEssays 42 (2020)
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