Generalized Procrustes Analysis (GPA)

methods / Representation Alignment / Generalized Procrustes Analysis (GPA)

Techniqueintermediate

Finds the optimal orthogonal transformation (rotation/reflection, no scaling or shearing) aligning one configuration of points onto another, then reports 1 minus the residual misalignment as a direct shape-similarity score — unlike RSA, this compares raw coordinate configurations rather than pairwise-distance matrices, so it is sensitive to genuine shape (not just relative distances).

Used in (3 observations)

Human perceptual geometry emerges transiently in middle LLM layersmeasured

structure: Circle · models: Llama-3-8B, Llama-3.2-3B, Gemma-7B, Qwen3-4B · paper: Geometry of Human Perceptual Domains Emerges Transiently in LLM Representations

Number-task subspaces are distinct yet linearly inter-transformablemeasured

structure: Linear Subspace, Linear Direction · models: BERT-base-uncased, GPT-2 Small, Qwen-2.5-7B, Qwen2.5-Math-7B · paper: The Representational Geometry of Number

Six Ekman emotion vectors in vision-language models have a low-dimensional geometry (PC1+PC2 explain 55-75% of variance), and a Procrustes-aligned consensus emotion subspace across three VLMs retains selective steering and transfers to held-out Gemma-3measured

structure: Linear Subspace · models: Qwen3-VL-8B-Instruct, InternVL3.5-8B-Instruct, Ministral-3-8B-Instruct-2512, Gemma 3 12B Instruct, Gemma 3 27B Instruct · paper: Do Emotion Concepts Generalize across Sources, Modalities, and Architectures in Vision-Language Models?