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

arXiv: https://arxiv.org/abs/2604.03147 · HTML: https://mlsanity.com/paper/2604.03147/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 53 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 30 of 34)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- [GoEmotions: A Dataset of Fine-Grained Emotions](https://mlsanity.com/paper/2005.00547/) (2020)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [Large Language Models Understand and Can be Enhanced by Emotional Stimuli](https://mlsanity.com/paper/2307.11760/) (2023)
- [Analyzing the Generalization and Reliability of Steering Vectors](https://mlsanity.com/paper/2407.12404/) (2024)
- [How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden States](https://mlsanity.com/paper/2406.05644/) (2024)
- [Style Vectors for Steering Generative Large Language Model](https://mlsanity.com/paper/2402.01618/) (2024)
- [Understanding (Un)Reliability of Steering Vectors in Language Models](https://mlsanity.com/paper/2505.22637/) (2025)
- [Navigating the OverKill in Large Language Models](https://mlsanity.com/paper/2401.17633/) (2024)
- [Shared Global and Local Geometry of Language Model Embeddings](https://mlsanity.com/paper/2503.21073/) (2025)
- [NRC VAD Lexicon v2: Norms for Valence, Arousal, and Dominance for over 55k English Terms](https://mlsanity.com/paper/2503.23547/) (2025)
- [Activation Space Interventions Can Be Transferred Between Large Language Models](https://mlsanity.com/paper/2503.04429/) (2025)
- [Towards Tracing Trustworthiness Dynamics: Revisiting Pre-training Period of Large Language Models](https://mlsanity.com/paper/2402.19465/) (2024)
- [NegativePrompt: Leveraging Psychology for Large Language Models Enhancement via Negative Emotional Stimuli](https://mlsanity.com/paper/2405.02814/) (2024)
- [Emotions Where Art Thou: Understanding and Characterizing the Emotional Latent Space of Large Language Models](https://mlsanity.com/paper/2510.22042/) (2025)
- [Refashioning Emotion Recognition Modelling: The Advent of Generalised Large Models](https://mlsanity.com/paper/2308.11578/) (2023)
- [Aligned but Blind: Alignment Increases Implicit Bias by Reducing Awareness of Race](https://mlsanity.com/paper/2506.00253/) (2025)
- [The Geometry of Self-Verification in a Task-Specific Reasoning Model](https://mlsanity.com/paper/2504.14379/) (2025)
- [Quantifying Valence and Arousal in Text with Multilingual Pre-trained Transformers](https://mlsanity.com/paper/2302.14021/) (2023)

## Built on by (most cited first, 16 of 16)

- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Latent Structure of Affective Representations in Large Language Models](https://mlsanity.com/paper/2604.07382/) (2026)
- [Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space](https://mlsanity.com/paper/2605.12412/) (2026)
- [Where Do Models Find Happiness? Emotion Vectors in Open-Source LLMs](https://mlsanity.com/paper/2606.26987/) (2026)
- [Tensor Product Representation Probes Reveal Shared Structure Across Linear Directions](https://mlsanity.com/paper/2605.09967/) (2026)
- [Probing for Representation Manifolds in Superposition](https://mlsanity.com/paper/2605.18537/) (2026)
- [Geometry of Human Perceptual Domains Emerges Transiently in LLM Representations](https://mlsanity.com/paper/2605.27970/) (2026)
- [Intrinsic Guardrails: How Semantic Geometry of Personality Interacts with Emergent Misalignment in LLMs](https://mlsanity.com/paper/2605.10633/) (2026)
- [VA-DPO: Valence-Arousal Direct Preference Optimization for Controllable Emotion Generation in Language Models](https://mlsanity.com/paper/2608.20374/) (2026)
- [Investigating Assistant Bias in LLM User Simulators Using a Role Vector](https://mlsanity.com/paper/2609.00608/) (2026)
- [Some Tokens Behave like Magnets: Revealing Linguistic Organization in the Layers of Language Models](https://mlsanity.com/paper/2609.05743/) (2026)
- [You Can't Prefer Emotions You Don't Sample: Intensity Undershoot in DPO-Tuned LLMs](https://mlsanity.com/paper/2609.07808/) (2026)
- [Empathy Is Steerable but Multi-Axial: Mechanism Geometry and Persona Effects in LLMs](https://mlsanity.com/paper/2609.15654/) (2026)
- [Replicating the Geometry of Emotion Representations in a Base Open-Weights Model](https://mlsanity.com/paper/2609.22208/) (2026)
- [EmoRSS: Mitigating Emotion-Induced Over-Refusal in Large Language Models](https://mlsanity.com/paper/2610.04998/) (2026)
- [Usage-Modulated Sentiment Representations in Large Language Models](https://mlsanity.com/paper/2610.05069/) (2026)

## 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.