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

2026/04/03 by Lihao Sun, Lewen Yan, Xiaoya Lu +3 · 1 voice
Computer Science · #cs.AI #cs.CL #cs.CY

paper · pdf · doi:10.48550/arxiv.2604.03147

arxiv published 2026/04/03 · arxiv updated 2026/05/08

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.

Citations

• Emotion Concepts and their Function in a Large Language Model
• Emotions Where Art Thou: Understanding and Characterizing the Emotional Latent Space of Large Language Models
• Emergence of Hierarchical Emotion Organization in Large Language Models
• Aligned but Blind: Alignment Increases Implicit Bias by Reducing Awareness of Race
• Understanding (Un)Reliability of Steering Vectors in Language Models
• AI with Emotions: Exploring Emotional Expressions in Large Language Models
• The Geometry of Self-Verification in a Task-Specific Reasoning Model
• NRC VAD Lexicon v2: Norms for Valence, Arousal, and Dominance for over 55k English Terms
• Shared Global and Local Geometry of Language Model Embeddings
• Activation Space Interventions Can Be Transferred Between Large Language Models
• From Rational Answers to Emotional Resonance: The Role of Controllable Emotion Generation in Language Models
• Analyzing the Generalization and Reliability of Steering Vectors
• WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs
• External Invariants: A Cryptographic Trust Architecture for Institutional AI Inference
• How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden States
• NegativePrompt: Leveraging Psychology for Large Language Models Enhancement via Negative Emotional Stimuli
• Towards Tracing Trustworthiness Dynamics: Revisiting Pre-training Period of Large Language Models
• HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal
• Style Vectors for Steering Generative Large Language Model
• Navigating the OverKill in Large Language Models
• The Good, The Bad, and Why: Unveiling Emotions in Generative AI
• Steering Llama 2 via Contrastive Activation Addition
• Instruction-Following Evaluation for Large Language Models
• Linear Representations of Sentiment in Large Language Models
• Representation Engineering: A Top-Down Approach to AI Transparency
• Refashioning Emotion Recognition Modelling: The Advent of Generalised Large Models
• Steering Language Models With Activation Engineering
• XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models
• Large Language Models Understand and Can be Enhanced by Emotional Stimuli
• Quantifying Valence and Arousal in Text with Multilingual Pre-trained Transformers
• Progress measures for grokking via mechanistic interpretability
• Discovering Language Model Behaviors with Model-Written Evaluations
• Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space
• Measuring Mathematical Problem Solving With the MATH Dataset
• GoEmotions: A Dataset of Fine-Grained Emotions

Cited by

• LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals

Discussions

• While we find consistent circular VA geometry across Llama and Qwen models, Anthropic concurrently finds similar structure in Claude. Check our work out! arxiv.org/abs/2604.03147 And thanks to all col [bsky, 2 points, 0 comments]

Related

• Do LLMs "Feel"? Emotion Circuits Discovery and Control
• How Emotion Shapes the Behavior of LLMs and Agents: A Mechanistic Study
• Emotions Where Art Thou: Understanding and Characterizing the Emotional Latent Space of Large Language Models
• Towards Emotion-Based Synthetic Consciousness: Using LLMs to Estimate Emotion Probability Vectors
• Emergence of Hierarchical Emotion Organization in Large Language Models