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

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.

Figures (7)

• Figure 1: Emotion steering vectors projected onto the VA subspace at layer 31, colored by valence. Gray circle: algebraic least-squares fit. The circular arrangement is analogous to circumplex model of affect in human psychology russell1980circumplex.
• Figure 2: Recovery of self-reported VA scores via correlation with learned subspace projections across layers. Solid lines: ridge regression over multiple PCs; dashed lines: best single PC.
• Figure 3: Radial heatmaps showing the effect of VA steering on open-ended generation. Each panel displays the change relative to unsteered baseline as a function of steering direction (angle) and strength (radius, $\alpha \in [0.01, 0.45]$). Cardinal directions: $0^\circ = +V$, $90^\circ = +A$, $180^\circ = -V$, $270^\circ = -A$. (a) Valence change (VAD-BERT). (b) Arousal change (VAD-BERT). (c) Sentiment change (VADER). The horizontal gradient in (a) and vertical gradient in (b) confirm the learned subspace enables controllable, geometrically predictable modulation of affect.
• Figure 4: Valence-arousal steering controls refusal behavior. Refusal rate as a function of signed steering strength $\alpha$ across three safety benchmarks. Steering along both valence (blue) and arousal (orange) directions bidirectionally modulates refusal rates, with negative $\alpha$ (decreasing V/A) increasing refusals and positive $\alpha$ (increasing V/A) suppressing them. Random directions within the representation space (gray) produce no systematic effect.
• Figure 5: Valence steering reduces sycophantic behavior. Sycophancy rate as a function of steering strength $\alpha$ across three benchmarks. Random steering directions (gray) remain near baseline with minimal variation.