The Information Geometry of Softmax: Probing and Steering

TL;DR

This paper explores how the geometry of softmax-based representations in AI models reflects semantic structure, introducing a dual steering method that improves concept control and stability.

Contribution

It introduces the use of information geometry for understanding softmax representations and proposes dual steering for robust semantic manipulation.

Findings

Dual steering enhances controllability of concepts.

Dual steering minimizes unintended changes to off-target concepts.

Information geometry effectively explains semantic encoding in softmax models.

Abstract

This paper concerns the question of how AI systems encode semantic structure into the geometric structure of their representation spaces. The motivating observation of this paper is that the natural geometry of these representation spaces should reflect the way models use representations to produce behavior. We focus on the important special case of representations that define softmax distributions. In this case, we argue that the natural geometry is information geometry. Our focus is on the role of information geometry on semantic encoding and the linear representation hypothesis. As an illustrative application, we develop "dual steering", a method for robustly steering representations to exhibit a particular concept using linear probes. We prove that dual steering optimally modifies the target concept while minimizing changes to off-target concepts. Empirically, we find that dual steering enhances the controllability and stability of concept manipulation.