# A Mathematical Theory of Agency and Intelligence

arXiv: https://arxiv.org/abs/2602.22519 · HTML: https://mlsanity.com/paper/2602.22519/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Cooperative Inverse Reinforcement Learning](https://mlsanity.com/paper/1606.03137/) (2016)
- [Empowerment -- an Introduction](https://mlsanity.com/paper/1310.1863/) (2013)
- [Managing extreme AI risks amid rapid progress](https://mlsanity.com/paper/2310.17688/) (2023)
- [Mutual Information Tracks Policy Coherence in Reinforcement Learning](https://mlsanity.com/paper/2509.10423/) (2025)
- [Entropy-Based Non-Invasive Reliability Monitoring of Convolutional Neural Networks](https://mlsanity.com/paper/2508.21715/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Informational Cost of Agency: A Bounded Measure of Interaction Efficiency for Deployed Reinforcement Learning](https://mlsanity.com/paper/2603.01283/) (2026)

## Abstract (arXiv)

To operate reliably under changing conditions, complex systems require feedback on how effectively they use resources, not just whether objectives are met. Current AI systems process vast information to produce sophisticated predictions, yet predictions can appear successful while the underlying interaction with the environment degrades. What is missing is a principled measure of how much of the total information a system deploys is actually shared between its observations, actions, and outcomes. We prove this shared fraction, which we term bipredictability, P, is intrinsic to any interaction, derivable from first principles, and strictly bounded: P can reach unity in quantum systems, P equal to, or smaller than 0.5 in classical systems, and lower once agency (action selection) is introduced. We confirm these bounds in a physical system (double pendulum), reinforcement learning agents, and multi turn LLM conversations. These results distinguish agency from intelligence: agency is the capacity to act on predictions, whereas intelligence additionally requires learning from interaction, self-monitoring of its learning effectiveness, and adapting the scope of observations, actions, and outcomes to restore effective learning. By this definition, current AI systems achieve agency but not intelligence. Inspired by thalamocortical regulation in biological systems, we demonstrate a feedback architecture that monitors P in real time, establishing a prerequisite for adaptive, resilient AI.