Action-Directed Information for Distributed Control and Agentic Interaction

Deployed reinforcement learning systems lack a principled runtime reliability theory. We close this gap by introducing Bipredictability, P, a closed form information theoretic metric that quantifies how efficiently a closed loop interaction between agent and environment converts uncertainty into shared predictability. P admits a provable classical bound P equal, smaller than 0.5, derived from Shannon entropy subadditivity, and responsive agency necessarily suppresses P below this ceiling, a structural prediction we term the informational cost of agency. Across 21 trained continuous control agents, we confirm this prediction empirically at P = 0.33 plus minus 0.02. The same suppression signature reproduces in language model dialogue, convolutional vision systems, and classical mechanical baselines, indicating that P captures a substrate independent property of agentic interaction rather than an algorithm specific artifact. The Information Digital Twin, IDT, a model agnostic architecture that computes P from the external interaction stream, detects 89.3% of coupling degradations against 44.0% for reward based monitoring, with 4.4 times lower latency. P provides the missing measurement layer for runtime reliability and closed loop self regulation in deployed autonomous systems.

We study agency under partial observability in deterministic physical or simulated worlds, where apparent randomness arises from uncertainty over initial conditions, fixed law bits, and unrolled exogenous noise. We model sensing and actuation as bridge interfaces split between agent-controlled parameters and environment-controlled channel state, inducing a deterministic POMDP through a prior over latent microstates and many-to-one observation coarsening. Within this framework, we prove a separation between prediction, compression, and empowerment. Perfect prediction can be achieved either by identifying the hidden quotient relevant to the target family or by overwrite control that makes the future target action-determined; high empowerment alone is insufficient. Under refinable interfaces and sufficient memory, action-conditioned observation-compression progress reduces posterior uncertainty about the latent quotient, and when refinement requires steering world-side channel conditions, this creates target-conditioned interface empowerment. A bit-string specialization with a conserved information budget makes the resulting tradeoff explicit: prediction by identification requires internal capacity at least the relevant latent entropy, whereas overwrite control requires terminal action capacity over the controlled quotient. For modern AI agents, the results suggest a design principle rather than a theorem of inevitability: objectives should distinguish hidden-state identification, interface refinement, task-relevant controllability, and mere overwrite or distractor control. Human--AI alignment is partly an interface-design problem, where the relevant bridge is between human intent, agent internal state, external tools, and world-side channel conditions. This is a working draft: feedback and criticism is most welcome.

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.