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 (2 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