Not All Latent Spaces Are Flat: Hyperbolic Concept Control

2026-03-14

AI Summary

This work addresses the challenge of unsafe content generation in state-of-the-art text-to-image (T2I) models, which, despite producing high-fidelity images, often lack reliable mechanisms for concept-level control. To this end, we propose Hyperbolic Concept Control (HyCon), the first approach to leverage hyperbolic geometry for concept manipulation in T2I synthesis. HyCon integrates a lightweight adapter that bridges off-the-shelf generative models with a hyperbolic text encoder, enabling stable and expressive control through parallel transport within a semantically aligned hyperbolic space. By transcending the limitations of conventional Euclidean-space adjustments, HyCon achieves state-of-the-art performance across four safety benchmarks and demonstrates consistent effectiveness on four mainstream T2I backbone architectures, underscoring its robustness and generalizability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Safety and Robustness
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

As modern text-to-image (T2I) models draw closer to synthesizing highly realistic content, the threat of unsafe content generation grows, and it becomes paramount to exercise control. Existing approaches steer these models by applying Euclidean adjustments to text embeddings, redirecting the generation away from unsafe concepts. In this work, we introduce hyperbolic control (HyCon): a novel control mechanism based on parallel transport that leverages semantically aligned hyperbolic representation space to yield more expressive and stable manipulation of concepts. HyCon reuses off-the-shelf generative models and a state-of-the-art hyperbolic text encoder, linked via a lightweight adapter. HyCon achieves state-of-the-art results across four safety benchmarks and four T2I backbones, showing that hyperbolic steering is a practical and flexible approach for more reliable T2I generation.

Problem

• text-to-image generation
• unsafe content
• concept control
• safety
• latent space

Innovation

• hyperbolic control
• parallel transport
• text-to-image generation
• concept steering
• safety alignment