Convex-hull clustering (DirectProbe)

methods / Theoretical / Analytical / Geometric analysis / Convex-hull clustering (DirectProbe)

Techniqueadvanced

Bottom-up agglomerative clustering that merges same-label points only while the convex hulls of different-label clusters remain provably disjoint (checked via a hyperplane-separation LP), producing the fewest convex regions consistent with the labeling — a classifier-free way to study representation geometry directly.

Used in (2 observations)

DirectProbe finds convex label clusters whose geometry predicts accuracymeasured

structure: Linear Separability · models: BERT-base-cased, BERT-large-cased, RoBERTa-base, RoBERTa-large, ELMo (5.5B-word pretrained, 2-layer biLSTM) · paper: DirectProbe: Studying Representations without Classifiers

Fine-tuning widens convex-cluster margins without rearranging the geometrymeasured

structure: Linear Separability · models: BERT-tiny, BERT-mini, BERT-small, BERT-medium, BERT-base-uncased · paper: A Closer Look at How Fine-tuning Changes BERT