Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch

ArXi:2605.03346v1 Announce Type: cross Embedding-based representations in Euclidean space $\mathbb{R}^d$ are a cornerstone of modern machine learning, where a major goal is to use the \emph{smallest dimension} that faithfully captures data relations. In this work, we prove sharp dimension--accuracy tradeoffs and identify a fundamental information-theoretic limitation: unless the embedding dimension $d$ is chosen close to the ground-truth dimension $D$, accuracy undergoes a sudden collapse.