# BiXSE: Improving Dense Retrieval via Probabilistic Graded Relevance Distillation

arXiv: https://arxiv.org/abs/2508.06781 · HTML: https://mlsanity.com/paper/2508.06781/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 57 references that are in the map.
- First posted on arXiv 9 Aug 2025.

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [BEIR: A Heterogenous Benchmark for Zero-shot Evaluation of Information Retrieval Models](https://mlsanity.com/paper/2104.08663/) (2021)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [ELI5: Long Form Question Answering](https://mlsanity.com/paper/1907.09190/) (2019)
- [ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction](https://mlsanity.com/paper/2112.01488/) (2021)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [RocketQA: An Optimized Training Approach to Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2010.08191/) (2020)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [One Embedder, Any Task: Instruction-Finetuned Text Embeddings](https://mlsanity.com/paper/2212.09741/) (2022)
- [Improving Text Embeddings with Large Language Models](https://mlsanity.com/paper/2401.00368/) (2023)
- [Promptagator: Few-shot Dense Retrieval From 8 Examples](https://mlsanity.com/paper/2209.11755/) (2022)
- [Generative Representational Instruction Tuning](https://mlsanity.com/paper/2402.09906/) (2024)
- [RocketQAv2: A Joint Training Method for Dense Passage Retrieval and Passage Re-ranking](https://mlsanity.com/paper/2110.07367/) (2021)
- [Improving Efficient Neural Ranking Models with Cross-Architecture Knowledge Distillation](https://mlsanity.com/paper/2010.02666/) (2020)

## Built on by (most cited first, 2 of 2)

- [MemReranker: Reasoning-Aware Reranking for Agent Memory Retrieval](https://mlsanity.com/paper/2605.06132/) (2026)
- [RALI@iKAT 2026: Retrieval-aware User Profile Denoising via Personalized Conversational Dense Retrieval](https://mlsanity.com/paper/2610.17673/) (2026)

## Abstract (arXiv)

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 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.