Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch
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. Our main result shows that this phenomenon arises even in standard contrastive learning settings, where supervision is limited to a set of $m$ anchor--positive--negative triplets $(i,j,k)$ encoding distance comparisons $\mathrm{dist}(i,j) < ...
| Authors | Dionysis Arvanitakis, Vaggos Chatziafratis, Yiyuan Luo |
|---|---|
| Primary category | cs.DS |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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