# Plasticity as the Mirror of Empowerment

arXiv: https://arxiv.org/abs/2505.10361 · HTML: https://mlsanity.com/paper/2505.10361/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 19 of 19)

- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Explore, Discover and Learn: Unsupervised Discovery of State-Covering Skills](https://mlsanity.com/paper/2002.03647/) (2020)
- [Loss of Plasticity in Continual Deep Reinforcement Learning](https://mlsanity.com/paper/2303.07507/) (2023)
- [Optimal Policies Tend to Seek Power](https://mlsanity.com/paper/1912.01683/) (2019)
- [A Definition of Continual Reinforcement Learning](https://mlsanity.com/paper/2307.11046/) (2023)
- [Continual Backprop: Stochastic Gradient Descent with Persistent Randomness](https://mlsanity.com/paper/2108.06325/) (2021)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Simple Agent, Complex Environment: Efficient Reinforcement Learning with Agent States](https://mlsanity.com/paper/2102.05261/) (2021)
- [Continual Learning as Computationally Constrained Reinforcement Learning](https://mlsanity.com/paper/2307.04345/) (2023)
- [Relative Variational Intrinsic Control](https://mlsanity.com/paper/2012.07827/) (2020)
- [Settling the Reward Hypothesis](https://mlsanity.com/paper/2212.10420/) (2022)
- [Characterizing AI Agents for Alignment and Governance](https://mlsanity.com/paper/2504.21848/) (2025)
- [Formalizing the Generalization-Forgetting Trade-off in Continual Learning](https://mlsanity.com/paper/2109.14035/) (2021)
- [Rethinking the Foundations for Continual Reinforcement Learning](https://mlsanity.com/paper/2504.08161/) (2025)
- [Three Dogmas of Reinforcement Learning](https://mlsanity.com/paper/2407.10583/) (2024)
- [Hierarchical Empowerment: Towards Tractable Empowerment-Based Skill Learning](https://mlsanity.com/paper/2307.02728/) (2023)
- [On the Convergence of Bounded Agents](https://mlsanity.com/paper/2307.11044/) (2023)

## Built on by (most cited first, 12 of 12)

- [Training LLM Agents to Empower Humans](https://mlsanity.com/paper/2510.13709/) (2025)
- [Towards Agentic Intelligence for Materials Science](https://mlsanity.com/paper/2602.00169/) (2026)
- [Unifying Goal-Conditioned RL and Unsupervised Skill Learning via Control-Maximization](https://mlsanity.com/paper/2605.06145/) (2026)
- [Artificial Agency Program: Curiosity, compression, and communication in agents](https://mlsanity.com/paper/2602.24100/) (2026)
- [What Is Worth Representing? Representational Empowerment for Continual Model Construction](https://mlsanity.com/paper/2609.02322/) (2026)
- [Ergodic Risk Measures: Towards a Risk-Aware Foundation for Continual Reinforcement Learning](https://mlsanity.com/paper/2510.02945/) (2025)
- [Prediction and Empowerment: A Theory of Agency through Bridge Interfaces](https://mlsanity.com/paper/2605.06346/) (2026)
- [Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning](https://mlsanity.com/paper/2606.25357/) (2026)
- [World models of environment, agent and joint agent-environment systems](https://mlsanity.com/paper/2608.20401/) (2026)
- [Efficient Exploration Is Enough](https://mlsanity.com/paper/2609.07575/) (2026)
- [A Bellman Optimality Equation for Plasticity](https://mlsanity.com/paper/2609.10776/) (2026)
- [Scaling Empowered Agents](https://mlsanity.com/paper/2610.13002/) (2026)

## Abstract (arXiv)

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. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result 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