A 40-dim SVD emotional subspace with four interpretable axes steers emotion

measured in 1 paper

Reichman et al. extract a low-dimensional emotional subspace from mean-pooled hidden states of Llama-3.1-8B, OLMo-2-7B and Ministral-8B via centered SVD, using its top 40 dimensions [reichman-etal-2025-emotional-latent-space-llms] The four leading PCs align with valence, dominance, approach-avoidance and arousal, stable across layers (Spearman up to 0.92 for emotion ordering) [reichman-etal-2025-emotional-latent-space-llms] A linear cross-domain alignment map generalizes the subspace across 8 emotion datasets in 6 languages (aligned-subspace cosine 0.83-0.94) [reichman-etal-2025-emotional-latent-space-llms] A trained one-layer MLP mapping the 40D projection to a residual shift raises target-emotion accuracy from 9% to 83% (English, Llama) while preserving semantics [reichman-etal-2025-emotional-latent-space-llms]

Structure

Linear Subspace

Context

40-dimensional centered-SVD emotional subspace with four interpretable PC axes (valence, dominance, approach-avoidance, arousal), cross-layer rank-correlation stability of PC-based emotion ordering, linear cross-domain/cross-lingual alignment (least-squares regression between per-dataset subspace fits), learned nonlinear (MLP) steering module built on a discovered linear subspace, not a raw direction-addition vector, competing/complementary geometric-shape claim relative to the circular and parabolic emotion-geometry findings already in this map

Confirmed in models

Llama-3.1-8B · Llama, Llama-3.1-8B-Instruct · Llama, OLMo 2 7B · OLMo 2, OLMo 2 7B Instruct · OLMo 2, Ministral-8B-Instruct-2410 · Mistral

Method

PCA, Linear probing, Representation Alignment

Papers

Emotions Where Art Thou: Characterizing the Emotional Latent Space of LLMs — Reichman, Benjamin, Avsian, Adar, Heck, Larry2025 · arXiv:2510.22042