Late-interaction models such as ColBERT achieve strong effectiveness by representing each document with many token-level vectors, but this expressivity leads to large indexing cost, storage footprints and expensive MaxSim scoring. We show that late-interaction representations exhibit an intrinsic low-rank structure: document token embeddings concentrate in a low-dimensional subspace that preserves most of the retrieval signal. Leveraging this observation, we introduce EigenLI, a spectral approximation framework that compresses late-interaction representations via document-specific low-dimensional subspaces. Unlike clustering or pooling methods, EigenLI identifies the dominant eigendirections of each document and uses them to construct reduced interaction representations. Empirically, k-EigenLI with k≤32 outperforms k-means and Ward clustering based pooling methods on ColBERTv2 and AnswerAI-ColBERT-small; GTE-ModernColBERT exhibits a different tradeoff at k=32, where clustering methods perform better. The same spectral construction also yields EigenLI-SV, an ANN-compatible single-vector representation derived from the second-order summary of the reduced structure. Across multiple datasets and all three text models, EigenLI-SV consistently outperforms comparable single-vector surrogates such as MUVERA.
While ColBERT is an effective neural retrieval architecture, it requires a heavy index structure to support candidate set retrieval based on approximated token embeddings, gathering and decompressing document token embeddings, and applying the MaxSim operation. Indexes in PLAID and similar ColBERT implementations require five to ten times the disk storage of the original raw text, which limits their scalability. Furthermore, prior work has identified that the gathering and decompression stages are the primary inefficiencies at query time. Limiting the number of document tokens that must be gathered by thresholding and score approximation does not eliminate the need for the entire index to support ad hoc queries. In this work, we propose an embedding quantization approach that turns a ColBERT index into a true inverted index. We show that, theoretically, ColBERT with embedding quantization is equivalent to learned-sparse retrieval except for the scoring mechanism. Empirically, we demonstrate that our index is 50-70% smaller than a one-bit PLAID index while retaining retrieval effectiveness.
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.