BACH: A Bayesian Admixture of Contrastive Heads for Multi-Interest Two-Tower Retrieval
Authors: Quoc Phong Nguyen, Paul Albert, Long Vuong, Vuong Le, Julien Monteil
Organizations: Amazon
Abstract
Two-tower retrievers compress each user into a single embedding, limiting their ability to serve diverse interests. Multi-interest models give each user several heads scored by a maximum inner product, but their hard-routing training under-utilizes heads (routing collapse) and gives no per-user estimate of how much each interest matters for serving. We present \textbf{BACH} (\emph{Bayesian Admixture of Contrastive Heads}), which casts multi-interest two-tower retrieval as a per-user mixture over the heads, fit by variational inference. The soft mixture trains every head (mitigating collapse), produces a per-user weighting of the interests that is reused at serving, and admits a shared global-codebook variant with precomputable retrieval. On three large-scale benchmarks, MovieLens-20M, Taobao, and Netflix, BACH improves top-of-ranking retrieval over hard-routing multi-interest and single-vector baselines at every head count; we further find that scoring every candidate by its best head, consistent with serving, outperforms the usual target-routed training, and that BACH improves further still.
We propose Latent Terms, a method revealing that models trained for dense retrieval, whether single- or multi-vector, learn representations that can trivially be decomposed into retrieval-ready sparse features. When trained on frozen retrievers, Sparse Autoencoders without any retrieval-specific adjustments extract a latent vocabulary with approximately Zipfian collection statistics, directly suitable for classical sparse retrieval scoring via BM25. This approach enables sparse retrieval while requiring no learned expansion objective or sparse retrieval supervision whatsoever, and can be readily applied to any dense retriever. Latent Terms is able to match or outperform single-vector scoring methods from its own base model as well as comparable SPLADE variants. In addition, it substantially outperforms its base model on LIMIT, a task specifically designed to highlight the failures of single-vector retrieval. Overall, our results highlight that neural retrievers contain more expressive and indexable structure than their default scoring functions expose, but that other methods can nonetheless be leveraged.
Multi-vector retrieval (MVR) models, exemplified by ColBERT, have established new benchmarks in retrieval accuracy by preserving fine-grained token-level interactions. However, this granularity imposes prohibitive storage and retrieval efficiency bottlenecks: to manage the immense memory footprint and computational overhead of billion-scale token vectors, state-of-the-art systems are forced to rely on aggressive dimension reduction and complex clustering (e.g., K-means). This compromise introduces two critical limitations: excessive indexing latency of clustering large-scale corpora and semantic information loss inherent to compression. In this paper, we propose Single-stage Sparse Retrieval (SSR}, a paradigm shift that replaces expensive clustering with efficient sparse coding. Instead of compressing features into low-dimensional dense vectors, we utilize Sparse Autoencoder (SAE) to project token embeddings into a high-dimensional but highly sparse representation. This transformation enables us to bypass vector clustering entirely and leverage inverted indexing for precise, high-throughput retrieval. Extensive experiments on the BEIR benchmark demonstrate that SSR achieves a "trifecta" of improvements: it reduces indexing time by 15x compared to ColBERTv2, halves retrieval latency, and simultaneously improves retrieval performance over leading baselines.
Multi-vector dense retrieval models, such as ColBERT, achieve strong retrieval effectiveness by modelling fine-grained token-level interactions between queries and documents. Methods such as PLAID use centroid-based quantisation of each token's vector to reduce the index size and speed up retrieval while maintaining strong effectiveness. In this work, we introduce PLAID-PRF, a method that performs Pseudo-Relevance Feedback (PRF) over PLAID to reformulate ColBERT's query vectors based on the top-retrieved results. In contrast with prior methods that perform PRF on multi-vector retrieval models, PLAID-PRF keeps computational costs low by leveraging the internal PLAID centroid vectors, treating them similarly to tokens in traditional PRF methods. The method selects a small and diverse set of high-utility expansion vectors and appends them to the original query, rerunning PLAID to refine both candidate generation and final scoring. Extensive experiments on the standard in-domain MSMARCO and four out-of-domain BEIR benchmarks show that PLAID-PRF consistently improves retrieval effectiveness over various baselines. In particular, PLAID-PRF improves over PLAID by up to 4.3% nDCG@10 and 7.3% MRR@10, while introducing substantially less computation overhead than prior PRF methods. The results demonstrate that our proposed centroid-aware PRF method offers an effective and lightweight mechanism to improve the quality of top-ranked retrieved results. Overall, this work enables effective and efficient feedback-aware late-interaction retrieval without expensive query-time document-token clustering.