Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Control

TL;DR

This paper reveals that emotion vectors in large language models are organized in a circular valence-arousal subspace, enabling monotonic and bidirectional control over generated text's affect and behaviors across multiple models.

Contribution

It uncovers the circular VA structure in LLM emotion vectors and demonstrates how VA steering can control multiple downstream behaviors from a single subspace.

Findings

Emotion vectors form a circular VA subspace in LLMs.

VA steering enables monotonic control over affective properties.

The effects are consistent across multiple LLM architectures.

Abstract

We show that emotion vectors in LLMs are organized by a two-dimensional valence-arousal (VA) subspace exhibiting circular geometry. Through principal component decomposition and ridge regression, we recover meaningful VA axes underlying emotion steering vectors whose projections correlate with human affect ratings across 44,728 words. Steering along these axes produces monotonic control over the affective properties of generated text, and further affords bidirectional control over multiple downstream behaviors (refusal and sycophancy) from a single subspace. These effects replicate across Llama-3.1-8B, Qwen3-8B, and Qwen3-14B. We propose lexical mediation to explain why these effects and prior emotionally framed controls work: refusal and compliance tokens occupy distinct VA regions, and VA steering directly modulates their emission probabilities.