Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Control
| Authors | Lihao Sun et al. |
| Year | 2026 |
| Field | NLP |
| arXiv | 2604.03147 |
| Download | |
| Categories | cs.CL, cs.AI, cs.CY |
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.
Engineering Breakdown
Plain English
This paper presents a method to extract and manipulate emotion dimensions (valence and arousal) directly within large language model representations. The authors trained on 211k emotion-labeled texts to derive steering vectors, then used ridge regression on the model's PCA components to learn linear VA axes that match human emotion perception. They validated their approach across 44k lexical items and demonstrated that steering along these axes produces monotonic shifts in model outputs—including the surprising finding that the same emotional dimensions can bidirectionally control refusal behavior and sycophancy. The recovered VA subspace exhibits circular geometry consistent with established psychological models of how humans perceive emotions.
Core Technical Contribution
The core novelty is discovering that valence-arousal dimensions form a interpretable linear subspace within LLM representations that (1) aligns with human crowdsourced emotion ratings and (2) enables robust steering of model behavior along continuous affective dimensions. Unlike prior work that treats emotion as a classification task, this approach identifies a geometric structure—a circular subspace—that mirrors the well-established circumplex model of emotion from psychology. The technical insight is that you can recover these dimensions through ridge regression on the model's self-reported VA scores projected onto PCA components of emotion steering vectors, yielding a parsimonious, interpretable steering mechanism. The finding that the same VA axes control both emotional tone and safety-relevant behaviors (refusal/sycophancy) suggests a deeper coupling between affect representation and model decision-making.
How It Works
The pipeline operates in three stages: (1) Data preparation: collect 211k emotion-labeled texts and generate emotion steering vectors from the model, (2) Dimensionality reduction: apply PCA to these steering vectors to identify the most salient directions in the emotion representation space, (3) Axis learning: use ridge regression to learn linear combinations of the top PCA components that predict the model's self-reported valence and arousal scores. The result is two learned weight vectors (VA axes) that define a 2D subspace embedded in the high-dimensional model representation space. During inference, you project hidden states onto these axes to measure or manipulate the model's emotional state, with steering strength controlled by a scalar coefficient. The circular geometry emerges naturally from this linear subspace and matches the circumplex model: moving along orthogonal axes smoothly transitions through the emotional space rather than jumping between discrete categories.
Production Impact
For production systems, this enables fine-grained control over model tone and personality without retraining, which is valuable for customer-facing applications (chatbots, customer service) and safety-critical systems. Concretely, you could implement a steering coefficient in your inference pipeline (minimal latency overhead—just linear projections) to control whether a model responds warmly or neutrally, or calibrate refusal thresholds by interpolating along the valence axis. The data requirements are moderate (211k labeled examples) compared to full fine-tuning, though you'll need to compute PCA and ridge regression once per model. The surprising bidirectional control over refusal/sycophancy suggests you could use emotion steering as a safety valve—e.g., pushing toward negative arousal to trigger more principled refusals. The main trade-off is that steering effectiveness likely degrades with model size and architecture variation; you'll need to validate the linear assumptions hold for your specific model and deployment context.
Limitations and When Not to Use This
The approach assumes that emotion-related information in LLMs is well-captured by linear combinations of PCA components, which may not hold for more complex, task-dependent emotional reasoning. The validation is limited to lexical items (44k word-level judgments) rather than longer, contextual passages where emotional interpretation is more nuanced and subjective. The paper does not thoroughly explore failure modes—what happens when the model lacks emotional grounding for certain domains, or when the circular geometry assumption breaks down? Additionally, the bidirectional refusal/sycophancy control is reported as 'near-monotonic' (not strictly monotonic), suggesting noise and potential edge cases in production deployment. The approach is model-specific; it's unclear whether VA axes learned on one LLM transfer to others, limiting generalizability across different model families and training procedures.
Research Context
This work builds on the circumplex model of emotion from psychology (Russel, 1980) and recent work in mechanistic interpretability showing that LLM representations contain interpretable linear subspaces for concepts like gender and sentiment. It extends prior work on steering vectors and activation engineering by focusing specifically on the continuous affective dimensions underlying human emotion perception. The paper contributes to the growing intersection of interpretability and safety—showing that emotional dimensions are not merely descriptive but mechanistically linked to safety-relevant behaviors. This opens future research directions into whether other psychological constructs (personality traits, moral reasoning) exhibit similar linear structure in LLMs, and whether understanding this geometry can improve alignment and robustness.
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