# The Geometry of Empowerment

arXiv: https://arxiv.org/abs/2610.07796 · HTML: https://mlsanity.com/paper/2610.07796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 21 of 21)

- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [Optimal Policies Tend to Seek Power](https://mlsanity.com/paper/1912.01683/) (2019)
- [C-Learning: Learning to Achieve Goals via Recursive Classification](https://mlsanity.com/paper/2011.08909/) (2020)
- [Variational Inverse Control with Events: A General Framework for Data-Driven Reward Definition](https://mlsanity.com/paper/1805.11686/) (2018)
- [Empowerment -- an Introduction](https://mlsanity.com/paper/1310.1863/) (2013)
- [Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making](https://mlsanity.com/paper/2406.17098/) (2024)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [The Information Geometry of Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2110.02719/) (2021)
- [Offline Goal-conditioned Reinforcement Learning with Quasimetric Representations](https://mlsanity.com/paper/2509.20478/) (2025)
- [Can a MISL Fly? Analysis and Ingredients for Mutual Information Skill Learning](https://mlsanity.com/paper/2412.08021/) (2024)
- [VIME: Variational Information Maximizing Exploration](https://mlsanity.com/paper/1605.09674/) (2016)
- [Episodic Novelty Through Temporal Distance](https://mlsanity.com/paper/2501.15418/) (2025)
- [Dual Goal Representations](https://mlsanity.com/paper/2510.06714/) (2025)
- [Learning to Assist Humans without Inferring Rewards](https://mlsanity.com/paper/2411.02623/) (2024)
- [Efficient Empowerment Estimation for Unsupervised Stabilization](https://mlsanity.com/paper/2007.07356/) (2020)
- [Which Features are Best for Successor Features?](https://mlsanity.com/paper/2502.10790/) (2025)
- [Training LLM Agents to Empower Humans](https://mlsanity.com/paper/2510.13709/) (2025)
- [Reward is not Necessary: How to Create a Modular & Compositional Self-Preserving Agent for Life-Long Learning](https://mlsanity.com/paper/2211.10851/) (2022)
- [Information-Theoretic Policy Pre-Training with Empowerment](https://mlsanity.com/paper/2510.05996/) (2025)
- [When Assisting One Disempowers Another](https://mlsanity.com/paper/2511.04177/) (2025)

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

- [Scaling Empowered Agents](https://mlsanity.com/paper/2610.13002/) (2026)

## Abstract (arXiv)

Empowerment captures the capacity for an agent to actively control its environment. While conceptually appealing as an information-theoretic quantity, the connection between empowerment and structurally central states that provide broad access to future outcomes has remained an open question. In this work, we link empowerment maximization and skill-learning methods to provide new geometries for interpreting and analyzing empowerment. Our analyses answer longstanding open questions on the connections between empowerment and structural centrality. Our analyses also reveal distinctions between information and reward geometries, highlighting important theoretical implications to build scalable empowerment-maximization methods. Website and code can be found at https://empowerment-geometry.github.io/.