In this paper, we provide a rigorous theoretical study of clustering with noisy queries. Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an oracle. Oracle can answer queries of the form ``do elements $u$ and $v$ belong to the same cluster?''-the

Among the state-of-the-art K-means approximation methods are the algorithms of Kanungo et al. and Ahmadian et al [

The success of contextual word representations and advances in neural information retrieval have made dense vector-based retrieval a standard approach for passage and document ranking. While effective and efficient, dual-encoders are brittle to variations in query distributions and noisy queries. Data augmentation can make models more robust but introduces overhead to training set generation and requires retraining and index regeneration. We present Contrastive Alignment POst Training (CAPOT), a highly efficient finetuning method that improves model robustness without requiring index regeneration, the training set optimization, or alteration. CAPOT enables robust retrieval by freezing the document encoder while the query encoder learns to align noisy queries with their unaltered root. We evaluate CAPOT noisy variants of MSMARCO, Natural Questions, and Trivia QA passage retrieval, finding CAPOT has a similar impact as data augmentation with none of its overhead.

In this paper, we provide a rigorous theoretical study of clustering with noisy queries. Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an oracle. Oracle can answer queries of the form do elements $u$ and $v$ belong to the same cluster?''-the In this paper, we provide the first information theoretic lower bound on the number of queries for clustering with noisy oracle in both situations. We design novel algorithms that closely match this query complexity lower bound, even when the number of clusters is unknown.