Organizations: Institute for Biomedical Informatics, University of Kentucky, Lexington, Kentucky, USA · Department of Computer Science, University of Kentucky, Lexington, Kentucky, USA
Abstract
Can intelligence be measured? We propose that intelligence can be defined as the lawful amplification of rare but valid futures: a system increases the probability of outcomes that would be unlikely under passive dynamics but remain admissible under the constraints of the domain. We start with the premise that an intelligent system must model the world and its own place within it. Because the system is part of the world it models, this leads naturally to recursive self-simulation: the system represents futures in which its own actions are part of the trajectory. Our central results give a necessity statement and a conditional near-sufficiency statement connecting this architecture to a precise thermodynamic measure of lawful amplification of rare-valid futures: high rare-valid lift is impossible unless the internal simulation identifies rare-valid futures with high fidelity; conversely, when rare-valid fidelity is high and the simulation contains an effective policy, the achievable lift approaches the actuation-limited optimum. Thus recursive self-simulation is not merely a plausible feature of intelligence but, under the stated assumptions, is necessary and nearly sufficient for high thermodynamic intelligence. The resulting framework makes intelligence measurable on a universal scale, from passive matter and feedback controllers, large language models, and humans as text generators to Maxwell-demon-like information engines.
The Legg--Hutter universal intelligence measure provides a rigorous scalar assessment of general intelligence as expected reward across all computable environments, weighted by simplicity. However, the measure presupposes an externally specified reward function, raising the question of whether the reward primitive is inherently arbitrary or whether a canonical choice exists. We propose a new measure, called intervention complexity, that has five natural properties: environment-derivedness, universality, minimality, sensitivity, and achievement preference. Given a resource function rho encoding an inductive bias (such as program length, execution time, or energy), rho-intervention complexity is a universal reward. The result yields a family of canonical rewards indexed by resource bias, providing a principled completion of the Legg--Hutter framework that does not require external normative input. We further propose a two-dimensional characterisation of intelligence: agent competence (how well the agent performs relative to the oracle optimum) and learning efficiency (how quickly this competence improves with experience). A separation theorem establishes that the choice of resource bias determines the computability of the resulting measure: action-count IC is computable in polynomial time, while program-length IC without oracle access is uncomputable, with the gap between oracle and bare IC precisely quantifying the information-theoretic content of learning. We discuss implications for superintelligence and for pre-training universal agents.
We develop a thermodynamic theory of algorithmic catalysis within the watts per intelligence framework, identifying reusable computational structures that reduce irreversible operations for a task class while satisfying bounded restoration and structural selectivity constraints. We prove that any class specific speed-up is upper-bounded by the algorithmic mutual information between the substrate and the class descriptor, and that encoding this information incurs a minimum thermodynamic cost via Landauer erasure. Combining these results yields a coupling theorem that lower-bounds the deployment horizon required for an algorithmic catalyst to be energetically favourable. The framework is illustrated on an affine SAT class and situates contemporary learned systems within an information thermodynamic constraint on intelligent computation.
How can we measure intelligence beyond human capability? Human-authored benchmarks saturate, and above human capability, examiners may not know which tasks are both hard and verifiable. We argue that this difficulty is inherent to absolute-scale evaluation and propose a new paradigm based on relative measurement in which models generate public challenges that separate other systems. Aggregating these outcomes yields an adversarial psychometric rating system that can scale with the systems being measured. We describe practical protocols that reduce incentives for private-information attacks, support judge-free adjudication, and naturally scale with agent capabilities. We instantiate the framework across verifiable and open-ended, non-verifiable domains, illustrating how model-generated evaluation can continue to measure systems beyond the human frontier.