Extend single-vector theoretical limits to multi-vector and other architectures

Extend the sign-rank-based theoretical framework for representational limits—developed for single-vector embedding models with dot-product scoring—to multi-vector retrieval architectures and other non-single-vector settings by establishing analogous lower and upper bounds on the required representation capacity.

Background

The paper’s theoretical results establish lower and upper bounds on representational capacity for single-vector embedding models using sign-rank and related rank notions. These results do not directly apply to other architectures such as multi-vector models.

The authors provide empirical evidence that multi-vector models behave differently on LIMIT but leave a formal extension of the theory to these architectures as future work.