The Informational Cost of Agency: A Bounded Measure of Interaction Efficiency for Deployed Reinforcement Learning

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.

How does a system that merely predicts the world come to distinguish its own causal influence from everything else? We trace this transition in a minimal 192-dimensional GRU through 40 controlled experiments arranged as a developmental sequence, adding components one at a time and tracking whether the system can distinguish self-caused from world-caused changes. The developmental path reveals four conditions that must be satisfied in strict order: (1) persistent state forming stable attractors, (2) a causal action loop linking output to input, (3) proprioceptive feedback that makes implicit causal knowledge explicit, and (4) asynchronous awakening - perceptual learning must consolidate before action learning begins. We propose agency gain (A = Err_world - Err_self), the predictive advantage of knowing one's own action, as a metric to track this process. The self-aware predictor consistently outperforms the self-blind predictor across periodic (sinusoidal) and chaotic (Lorenz) environments, and the metric survives ablation of all auxiliary components. Only forward-sampled action selection produces meaningful agency gain; two gradient-based alternatives degenerate. Equally significant are 12 falsified hypotheses mapping where development stalls: predictive coding alone does not produce self-represent

Large language model (LLM) agentic systems increasingly rely on models communicating with one another, yet existing uncertainty and multi-agent methods rarely estimate how a particular receiver will interpret a message before it is sent. This matters in heterogeneous systems, where capable receivers can reconstruct different tasks from the same message. We model this as a sender-receiver problem with a latent receiver type and define prospective interpretation risk (PIR): the probability that a receiver reconstructs a task other than intended. Rather than model an LLM's full input-output behaviour, we use black-box probes relating messages, intended tasks, and receiver-specific reconstructions, yielding scalable supervision while separating interpretation from downstream capability failure. Offline, heterogeneous frozen receivers provide supervision for receiver-conditioned risk and the effects of predefined mutable message features. At deployment, history induces a posterior over receiver types, guiding message revision and selection. We introduce value of interpretation information (VoII), querying for receiver information only when its expected communication benefit exceeds its cost. Our theory characterises when receiver information has decision value and bounds such queries. Empirically, interpretation-failure rates vary by 4-13x across receivers. Receiver information reduces PIR calibration error by 68% relative to a receiver-agnostic predictor, largely by correcting receiver-specific risk levels. PIR-guided revision reduces interpretation failure by 44% relative to the original message and 40% relative to a generic rewrite, mostly through a repair that helps every receiver. VoII outperforms information-gain and random querying at matched cost on the interpretation objective it optimises, lowering interpretation failure from 3.84% to 3.79% while querying 18.2% of episodes.