# SetRank: Learning a Permutation-Invariant Ranking Model for Information Retrieval

arXiv: https://arxiv.org/abs/1912.05891 · HTML: https://mlsanity.com/paper/1912.05891/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 30 of 48)

- [Lero: A Learning-to-Rank Query Optimizer](https://mlsanity.com/paper/2302.06873/) (2023)
- [Discrete Conditional Diffusion for Reranking in Recommendation](https://mlsanity.com/paper/2308.06982/) (2023)
- [Non-autoregressive Generative Models for Reranking Recommendation](https://mlsanity.com/paper/2402.06871/) (2024)
- [Quality-Aware Network for Human Parsing](https://mlsanity.com/paper/2103.05997/) (2021)
- [PEAR: Personalized Re-ranking with Contextualized Transformer for Recommendation](https://mlsanity.com/paper/2203.12267/) (2022)
- [Exploring Dense Retrieval for Dialogue Response Selection](https://mlsanity.com/paper/2110.06612/) (2021)
- [Learnable Pillar-based Re-ranking for Image-Text Retrieval](https://mlsanity.com/paper/2304.12570/) (2023)
- [RankFormer: Listwise Learning-to-Rank Using Listwide Labels](https://mlsanity.com/paper/2306.05808/) (2023)
- [Rank-LIME: Local Model-Agnostic Feature Attribution for Learning to Rank](https://mlsanity.com/paper/2212.12722/) (2022)
- [Set-to-Sequence Methods in Machine Learning: a Review](https://mlsanity.com/paper/2103.09656/) (2021)
- [ULTRA: An Unbiased Learning To Rank Algorithm Toolbox](https://mlsanity.com/paper/2108.05073/) (2021)
- [Learning To Rank Diversely At Airbnb](https://mlsanity.com/paper/2210.07774/) (2022)
- [NLGR: Utilizing Neighbor Lists for Generative Rerank in Personalized Recommendation Systems](https://mlsanity.com/paper/2502.06097/) (2025)
- [NR4DER: Neural Re-ranking for Diversified Exercise Recommendation](https://mlsanity.com/paper/2506.06341/) (2025)
- [Optimizing User Profiles via Contextual Bandits for Retrieval-Augmented LLM Personalization](https://mlsanity.com/paper/2601.12078/) (2026)
- [Set2setRank: Collaborative Set to Set Ranking for Implicit Feedback based Recommendation](https://mlsanity.com/paper/2105.07377/) (2021)
- [CODER: An efficient framework for improving retrieval through COntextual Document Embedding Reranking](https://mlsanity.com/paper/2112.08766/) (2021)
- [Learning List-Level Domain-Invariant Representations for Ranking](https://mlsanity.com/paper/2212.10764/) (2022)
- [GReF: A Unified Generative Framework for Efficient Reranking via Ordered Multi-token Prediction](https://mlsanity.com/paper/2510.25220/) (2025)
- [ListConRanker: A Contrastive Text Reranker with Listwise Encoding](https://mlsanity.com/paper/2501.07111/) (2025)
- [The Evolution of Reranking Models in Information Retrieval: From Heuristic Methods to Large Language Models](https://mlsanity.com/paper/2512.16236/) (2025)
- [Efficient Personalized Reranking with Semi-Autoregressive Generation and Online Knowledge Distillation](https://mlsanity.com/paper/2603.07107/) (2026)
- [Modeling Relevance Ranking under the Pre-training and Fine-tuning Paradigm](https://mlsanity.com/paper/2108.05652/) (2021)
- [MA4DIV: Multi-Agent Reinforcement Learning for Search Result Diversification](https://mlsanity.com/paper/2403.17421/) (2024)
- [TacoERE: Cluster-aware Compression for Event Relation Extraction](https://mlsanity.com/paper/2405.06890/) (2024)
- [JDRec: Practical Actor-Critic Framework for Online Combinatorial Recommender System](https://mlsanity.com/paper/2207.13311/) (2022)
- [Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding](https://mlsanity.com/paper/2301.03765/) (2023)
- [Pretrained deep models outperform GBDTs in Learning-To-Rank under label scarcity](https://mlsanity.com/paper/2308.00177/) (2023)
- [Multimodal Label Relevance Ranking via Reinforcement Learning](https://mlsanity.com/paper/2407.13221/) (2024)
- [Towards Principled Learning for Re-ranking in Recommender Systems](https://mlsanity.com/paper/2504.04188/) (2025)

## Abstract (arXiv)

In learning-to-rank for information retrieval, a ranking model is automatically learned from the data and then utilized to rank the sets of retrieved documents. Therefore, an ideal ranking model would be a mapping from a document set to a permutation on the set, and should satisfy two critical requirements: (1)~it should have the ability to model cross-document interactions so as to capture local context information in a query; (2)~it should be permutation-invariant, which means that any permutation of the inputted documents would not change the output ranking. Previous studies on learning-to-rank either design uni-variate scoring functions that score each document separately, and thus failed to model the cross-document interactions; or construct multivariate scoring functions that score documents sequentially, which inevitably sacrifice the permutation invariance requirement. In this paper, we propose a neural learning-to-rank model called SetRank which directly learns a permutation-invariant ranking model defined on document sets of any size. SetRank employs a stack of (induced) multi-head self attention blocks as its key component for learning the embeddings for all of the retrieved documents jointly. The self-attention mechanism not only helps SetRank to capture the local context information from cross-document interactions, but also to learn permutation-equivariant representations for the inputted documents, which therefore achieving a permutation-invariant ranking model. Experimental results on three large scale benchmarks showed that the SetRank significantly outperformed the baselines include the traditional learning-to-rank models and state-of-the-art Neural IR models.