Simple Projection Variants Improve ColBERT Performance

Multi-vector dense retrieval methods like ColBERT systematically use a single-layer linear projection to reduce the dimensionality of individual vectors. In this study, we explore the implications of the MaxSim operator on the gradient flows of the training of multi-vector models and show that such a simple linear projection has inherent, if non-critical, limitations in this setting. We then discuss the theoretical improvements that could result from replacing this single-layer projection with well-studied alternative feedforward linear networks (FFN), such as deeper, non-linear FFN blocks, GLU blocks, and skip-connections, could alleviate these limitations. Through the design and systematic evaluation of alternate projection blocks, we show that better-designed final projections positively impact the downstream performance of ColBERT models. We highlight that many projection variants outperform the original linear projections, with the best-performing variants increasing average performance on a range of retrieval benchmarks across domains by over 2 NDCG@10 points. We then conduct further exploration on the individual parameters of these projections block in order to understand what drives this empirical performance, highlighting the particular importance of upscaled intermediate projections and residual connections. As part of these ablation studies, we show that numerous suboptimal projection variants still outperform the traditional single-layer projection across multiple benchmarks, confirming our hypothesis. Finally, we observe that this effect is consistent across random seeds, further confirming that replacing the linear layer of ColBERT models is a robust, drop-in upgrade.

BMX: Entropy-weighted Similarity and Semantic-enhanced Lexical Search

BM25, a widely-used lexical search algorithm, remains crucial in information retrieval despite the rise of pre-trained and large language models (PLMs/LLMs). However, it neglects query-document similarity and lacks semantic understanding, limiting its performance. We revisit BM25 and introduce BMX, a novel extension of BM25 incorporating entropy-weighted similarity and semantic enhancement techniques. Extensive experiments demonstrate that BMX consistently outperforms traditional BM25 and surpasses PLM/LLM-based dense retrieval in long-context and real-world retrieval benchmarks. This study bridges the gap between classical lexical search and modern semantic approaches, offering a promising direction for future information retrieval research. The reference implementation of BMX can be found in Baguetter, which was created in the context of this work. The code can be found here: https://github.com/mixedbread-ai/baguetter.