Emotion representations trace a V-shaped open manifold with neutral at the vertex

measured in 1 paper

Choi & Weber build a classification-accuracy dissimilarity matrix from pairwise probes across GoEmotions categories at every layer of Gemma-2-9B and Mistral-7B, embedding it via MDS/Isomap/UMAP and Procrustes-aligning to human valence-arousal norms [choi-weber-2026-affective-structure] The recovered layout is a V-shaped parabolic open curve (an open 1-manifold, H1=0) with neutral at the vertex and positive/negative valence fanning out, rather than the classical circular circumplex [choi-weber-2026-affective-structure] Isomap's geodesic-to-Euclidean distance ratio (1.00-1.80 Gemma, 0.80-1.42 Mistral) confirms the curvature is real but modest [choi-weber-2026-affective-structure] Adding probe-direction vectors to Llama-3-70B-Instruct shifts human-rated output valence strongly (mean 7.29 vs 1.08 on a 10-point scale for positive versus negative targets) [choi-weber-2026-affective-structure]

Structure

1D continuum manifold, Linear Direction

Context

emotion, valence, arousal, parabolic manifold, vertex/neutral point, competing geometric claim, Procrustes alignment, human norm ground truth

Confirmed in models

Gemma-2-9B · Gemma, Mistral-7B · Mistral, Llama-3-70B-Instruct · Llama

Method

Linear probing, Isomap, UMAP, Activation Steering (Addition)

Papers

Latent Structure of Affective Representations in Large Language Models — Choi, Benjamin J., Weber, Melanie2026 · arXiv:2604.07382