Concept Algebra for (Score-Based) Text-Controlled Generative Models

TL;DR

This paper introduces a formal framework for understanding and manipulating concepts in score-based text-guided generative models by representing concepts as subspaces within the model's internal representations, enabling algebraic concept manipulation.

Contribution

It formalizes the concept of subspace representations in generative models and provides a simple method to identify and manipulate these concept subspaces.

Findings

Concepts are encoded as subspaces in the representation space.

A method to identify concept subspaces in models like Stable Diffusion.

Algebraic manipulation of concepts enables controlled generation.

Abstract

This paper concerns the structure of learned representations in text-guided generative models, focusing on score-based models. A key property of such models is that they can compose disparate concepts in a `disentangled' manner. This suggests these models have internal representations that encode concepts in a `disentangled' manner. Here, we focus on the idea that concepts are encoded as subspaces of some representation space. We formalize what this means, show there's a natural choice for the representation, and develop a simple method for identifying the part of the representation corresponding to a given concept. In particular, this allows us to manipulate the concepts expressed by the model through algebraic manipulation of the representation. We demonstrate the idea with examples using Stable Diffusion. Code in https://github.com/zihao12/concept-algebra-code