Blowfish: Topological and statistical signatures for quantifying ambiguity in semantic search

This works reports evidence for the topological signatures of ambiguity in sentence embeddings that could be leveraged for ranking and/or explanation purposes in the context of vector search and Retrieval Augmented Generation (RAG) systems. We proposed a working definition of ambiguity and designed an experiment where we have broken down a proprietary dataset into collections of chunks of varying size - 3, 5, and 10 lines and used the different collections successively as queries and answers sets. It allowed us to test the signatures of ambiguity with removal of confounding factors. Our results show that proxy ambiguous queries (size 10 queries against size 3 documents) display different distributions of homologies 0 and 1 based features than proxy clear queries (size 5 queries against size 10 documents). We then discuss those results in terms increased manifold complexity and/or approximately discontinuous embedding sub-manifolds. Finally we propose a strategy to leverage those findings as a new scoring strategy of semantic similarities.