$\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval
This paper studies the minimal dimension required to embed subset memberships ($m$ elements and ${m\choose k}$ subsets of at most $k$ elements) into vector spaces, denoted as Minimal Embeddable Dimension (MED). The tight bounds of MED are derived theoretically and supported empirically for various n…