Archetypal Analysis / Simplex Fitting (AANet)

methods / Dimensionality Reduction / Archetypal Analysis / Simplex Fitting (AANet)

Archetypal Analysis / Simplex Fitting (AANet)

Techniqueadvanced

Fits a K-vertex simplex to a point cloud by learning extreme points (archetypes) whose convex hull contains the data and re-expresses each point by its barycentric coordinates with respect to those archetypes, via a neural archetypal-analysis autoencoder (AANet).

Used in (2 observations)

SAE latents in Gemma-2-9B show preliminary simplex-structured belief geometrymeasured

structure: Belief State Geometry Hypothesis (Mixed-State Presentation), Polytope (Simplex) · models: Gemma-2-9B · paper: Finding Belief Geometries with Sparse Autoencoders

DINOv2 activation space is consistent with a Minkowski sum of tile polytopesargued

structure: Minkowski Sum of Tile Polytopes (Minkowski Representation Hypothesis) · models: DINOv2-B (ViT-Base, 4 register tokens) · paper: Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry