mlsanityData to 7 Oct 2026

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

arXiv 2604.03147 ↗First posted 3 Apr 2026cs.CL cs.AI cs.CYcited by 12

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 34 of its 53 references that are in the map. First posted on arXiv 3 Apr 2026.

Builds on

34 of 53 references.

References · 34

  1. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  2. 2024HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusalcited by 1,330
  3. 2023Representation Engineering: A Top-Down Approach to AI Transparencycited by 1,239
  4. 2023Instruction-Following Evaluation for Large Language Modelscited by 1,143
  5. 2023Steering Llama 2 via Contrastive Activation Additioncited by 1,009
  6. 2024Refusal in Language Models Is Mediated by a Single Directioncited by 960
  7. 2023Steering Language Models With Activation Engineeringcited by 824
  8. 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
  9. 2022Discovering Language Model Behaviors with Model-Written Evaluationscited by 805
  10. 2022Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Spacecited by 522
  11. 2020GoEmotions: A Dataset of Fine-Grained Emotionscited by 479
  12. 2023XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Modelscited by 477
22 more
  1. 2024WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMscited by 460
  2. 2023Linear Representations of Sentiment in Large Language Modelscited by 157
  3. 2023Large Language Models Understand and Can be Enhanced by Emotional Stimulicited by 143
  4. 2024Analyzing the Generalization and Reliability of Steering Vectorscited by 130
  5. 2024How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden Statescited by 92
  6. 2024Style Vectors for Steering Generative Large Language Modelcited by 56
  7. 2024Navigating the OverKill in Large Language Modelscited by 40
  8. 2025Understanding (Un)Reliability of Steering Vectors in Language Modelscited by 39
  9. 2025Shared Global and Local Geometry of Language Model Embeddingscited by 34
  10. 2025NRC VAD Lexicon v2: Norms for Valence, Arousal, and Dominance for over 55k English Termscited by 25
  11. 2024Towards Tracing Trustworthiness Dynamics: Revisiting Pre-training Period of Large Language Modelscited by 18
  12. 2024NegativePrompt: Leveraging Psychology for Large Language Models Enhancement via Negative Emotional Stimulicited by 18
  13. 2025Activation Space Interventions Can Be Transferred Between Large Language Modelscited by 17
  14. 2023Refashioning Emotion Recognition Modelling: The Advent of Generalised Large Modelscited by 16
  15. 2025Aligned but Blind: Alignment Increases Implicit Bias by Reducing Awareness of Racecited by 15
  16. 2025Emotions Where Art Thou: Understanding and Characterizing the Emotional Latent Space of Large Language Modelscited by 14
  17. 2025The Geometry of Self-Verification in a Task-Specific Reasoning Modelcited by 12
  18. 2023Quantifying Valence and Arousal in Text with Multilingual Pre-trained Transformerscited by 11
  19. 2023The Good, The Bad, and Why: Unveiling Emotions in Generative AIcited by 10
  20. 2025AI with Emotions: Exploring Emotional Expressions in Large Language Modelscited by 10
  21. 2025Emergence of Hierarchical Emotion Organization in Large Language Modelscited by 6
  22. 2025From Rational Answers to Emotional Resonance: The Role of Controllable Emotion Generation in Language Modelscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 12.

12 papers.

  1. 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 18
  2. 2026Latent Structure of Affective Representations in Large Language Modelscited by 3
  3. 2026Geometry of Human Perceptual Domains Emerges Transiently in LLM Representationscited by 1
  4. 2026Where Do Models Find Happiness? Emotion Vectors in Open-Source LLMscited by 1
  5. 2026Tensor Product Representation Probes Reveal Shared Structure Across Linear Directionscited by 0
  6. 2026Intrinsic Guardrails: How Semantic Geometry of Personality Interacts with Emergent Misalignment in LLMscited by 0
  7. 2026Probing for Representation Manifolds in Superpositioncited by 0
  8. 2026VA-DPO: Valence-Arousal Direct Preference Optimization for Controllable Emotion Generation in Language Modelscited by 0
  9. 2026Investigating Assistant Bias in LLM User Simulators Using a Role Vectorcited by 0
  10. 2026Some Tokens Behave like Magnets: Revealing Linguistic Organization in the Layers of Language Modelscited by 0
  11. 2026You Can't Prefer Emotions You Don't Sample: Intensity Undershoot in DPO-Tuned LLMscited by 0
  12. 2026Empathy Is Steerable but Multi-Axial: Mechanism Geometry and Persona Effects in LLMscited by 0