The Geometry of Empowerment

arXiv:2610.07796v1 Announce Type: new Abstract: 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/.