2604.00570 Dimensional Decomposition for Many-to-Many Matching in Embedding Spaces
Current embedding-based matching systems collapse multi-dimensional similarity into a single scalar score, conflating dimensions that should be independently queryable. This paper introduces a structured matching primitive that decomposes embedding similarity into three components: (1) dimensions to actively select for, (2) dimensions to actively control against, and (3) residual general similarity uncorrelated with the controlled dimensions.