BiXSE: Improving Dense Retrieval via Probabilistic Graded Relevance Distillation

Christos Tsirigotis, Vaibhav Adlakha, Joao Monteiro, Aaron Courville, Perouz Taslakian

Keywords: sentence embeddings, dense retrieval, retrieval, ranking, synthetic data

TL;DR: We propose an effective training method on synthetic graded relevance scores for improving dense encoders

Abstract: Neural sentence embedding models for dense retrieval typically rely on binary relevance labels, treating query-document pairs as either relevant or irrelevant. However, real-world relevance often exists on a continuum, and recent advances in large language models (LLMs) have made it feasible to scale the generation of fine-grained graded relevance labels. In this work, we propose \textbf{BiXSE}, a simple and effective pointwise training method that optimizes binary cross-entropy (BCE) over LLM-generated graded relevance scores. BiXSE interprets these scores as probabilistic targets, enabling granular supervision from a single labeled query-document pair per query. Unlike pairwise or listwise losses that require multiple annotated comparisons per query, BiXSE achieves strong performance with reduced annotation and compute costs by leveraging in-batch negatives. Extensive experiments across sentence embedding (MMTEB) and retrieval benchmarks (BEIR, TREC-DL) show that BiXSE consistently outperforms softmax-based contrastive learning (InfoNCE), and matches or exceeds strong pairwise ranking baselines when trained on LLM-supervised data. BiXSE offers a robust, scalable alternative for training dense retrieval models as graded relevance supervision becomes increasingly accessible.

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Submission Number: 1727