Plasticity as the Mirror of Empowerment

2025-05-15

AI Summary

This paper addresses the foundational question of how agents are shaped by observable information, introducing “plasticity” as a universal measure of an agent’s susceptibility to environmental influence. Method: We formally define plasticity for the first time, propose generalized directed information, and rigorously extend Massey’s directed information. Contribution/Results: We prove that plasticity and empowerment constitute a dual relationship: an agent’s plasticity equals the environment’s empowerment—mathematically equivalent and mirror-symmetric. This duality reveals an intrinsic tension between learning capacity and autonomy, fundamentally reconceptualizing agency within information theory. The result yields a computationally tractable theoretical principle for balancing perceptual sensitivity against behavioral autonomy, with foundational implications for artificial intelligence and cognitive science.

Technology Category

• Machine Learning: Information Theory
• Multiagent Systems: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Our first finding is that plasticity is the mirror of empowerment: The agent's plasticity is identical to the empowerment of the environment, and vice versa. Our second finding establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency.

Problem

• Defining agent plasticity as a universal measure of influence from observations
• Establishing plasticity as the mirror concept to empowerment in agents
• Exploring the tension between plasticity and empowerment in agent design

Innovation

• Introduces plasticity as agent-centric universal measure
• Defines plasticity using generalized directed information
• Reveals plasticity-empowerment mirror relationship and tension