# LogiCoL: Logically-Informed Contrastive Learning for Set-based Dense Retrieval

arXiv: https://arxiv.org/abs/2505.19588 · HTML: https://mlsanity.com/paper/2505.19588/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [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)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Reading Wikipedia to Answer Open-Domain Questions](https://mlsanity.com/paper/1704.00051/) (2017)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [KILT: a Benchmark for Knowledge Intensive Language Tasks](https://mlsanity.com/paper/2009.02252/) (2020)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [Efficiently Teaching an Effective Dense Retriever with Balanced Topic Aware Sampling](https://mlsanity.com/paper/2104.06967/) (2021)
- [A Logic-Driven Framework for Consistency of Neural Models](https://mlsanity.com/paper/1909.00126/) (2019)
- [Joint Constrained Learning for Event-Event Relation Extraction](https://mlsanity.com/paper/2010.06727/) (2020)
- [Augmenting Neural Networks with First-order Logic](https://mlsanity.com/paper/1906.06298/) (2019)
- [QUEST: A Retrieval Dataset of Entity-Seeking Queries with Implicit Set Operations](https://mlsanity.com/paper/2305.11694/) (2023)
- [NevIR: Negation in Neural Information Retrieval](https://mlsanity.com/paper/2305.07614/) (2023)
- [MoDE: CLIP Data Experts via Clustering](https://mlsanity.com/paper/2404.16030/) (2024)
- [Chain-of-Factors Paper-Reviewer Matching](https://mlsanity.com/paper/2310.14483/) (2023)
- [BoolQuestions: Does Dense Retrieval Understand Boolean Logic in Language?](https://mlsanity.com/paper/2411.12235/) (2024)
- [Global Contrastive Batch Sampling via Optimization on Sample Permutations](https://mlsanity.com/paper/2210.12874/) (2022)
- [SetBERT: Enhancing Retrieval Performance for Boolean Logic and Set Operation Queries](https://mlsanity.com/paper/2406.17282/) (2024)
- [Constructing Set-Compositional and Negated Representations for First-Stage Ranking](https://mlsanity.com/paper/2501.07679/) (2025)

## Built on by (most cited first, 3 of 3)

- [Retrieving Climate Change Disinformation by Narrative](https://mlsanity.com/paper/2603.22015/) (2026)
- [NSFL: A Post-Training Neuro-Symbolic Fuzzy Logic Framework for Boolean Operators in Neural Embeddings](https://mlsanity.com/paper/2604.10604/) (2026)
- [Reproducing Complex Set-Compositional Information Retrieval](https://mlsanity.com/paper/2605.03824/) (2026)

## Abstract (arXiv)

While significant progress has been made with dual- and bi-encoder dense retrievers, they often struggle on queries with logical connectives, a use case that is often overlooked yet important in downstream applications. Current dense retrievers struggle with such queries, such that the retrieved results do not respect the logical constraints implied in the queries. To address this challenge, we introduce LogiCoL, a logically-informed contrastive learning objective for dense retrievers. LogiCoL builds upon in-batch supervised contrastive learning, and learns dense retrievers to respect the subset and mutually-exclusive set relation between query results via two sets of soft constraints expressed via t-norm in the learning objective. We evaluate the effectiveness of LogiCoL on the task of entity retrieval, where the model is expected to retrieve a set of entities in Wikipedia that satisfy the implicit logical constraints in the query. We show that models trained with LogiCoL yield improvement both in terms of retrieval performance and logical consistency in the results. We provide detailed analysis and insights to uncover why queries with logical connectives are challenging for dense retrievers and why LogiCoL is most effective.