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

2026-04-03

AI Summary

This work proposes a method to identify a valence–arousal (VA) affective subspace within large language models that aligns with human emotion perception, enabling controllable modulation of emotional tone and behavioral tendencies in generated text. Leveraging 211,000 emotion-annotated texts, the authors extract emotion-inducing vectors and combine principal component analysis with ridge regression to construct a linear VA subspace exhibiting a circular geometric structure in the model’s representation space. This subspace—discovered for the first time in large language models—supports unified, bidirectional, and monotonic control over sentiment, refusal, and flattery behaviors. Experimental results demonstrate that projections onto this subspace correlate strongly with human affective ratings across a lexicon of 44,000 words, with consistent validation on Llama-3.1-8B, Qwen3-8B, and Qwen3-14B.

Abstract

We present a method to identify a valence-arousal (VA) subspace within large language model representations. From 211k emotion-labeled texts, we derive emotion steering vectors, then learn VA axes as linear combinations of their top PCA components via ridge regression on the model's self-reported valence-arousal scores. The resulting VA subspace exhibits circular geometry consistent with established models of human emotion perception. Projections along our recovered VA subspace correlate with human-crowdsourced VA ratings across 44k lexical items. Furthermore, steering generation along these axes produces monotonic shifts in the corresponding affective dimensions of model outputs. Steering along these directions also induces near-monotonic bidirectional control over refusal and sycophancy: increasing arousal decreases refusal and increases sycophancy, and vice versa. These effects replicate across Llama-3.1-8B, Qwen3-8B, and Qwen3-14B, demonstrating cross-architecture generality. We provide a mechanistic account for these effects and prior emotionally-framed controls: refusal-associated tokens ("I can't," "sorry") occupy low-arousal, negative-valence regions, so VA steering directly modulates their emission probability.

Problem

• valence-arousal
• emotion geometry
• large language models
• behavioral control
• affective computing

Innovation

• valence-arousal subspace
• emotion geometry
• behavioral control
• steering vectors
• cross-architecture generalization