# Set-LLM: A Permutation-Invariant LLM

arXiv: https://arxiv.org/abs/2505.15433 · HTML: https://mlsanity.com/paper/2505.15433/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 58 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [No Language Left Behind: Scaling Human-Centered Machine Translation](https://mlsanity.com/paper/2207.04672/) (2022)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [Multi-News: a Large-Scale Multi-Document Summarization Dataset and Abstractive Hierarchical Model](https://mlsanity.com/paper/1906.01749/) (2019)

## Built on by (most cited first, 11 of 11)

- [Stable-RAG: Mitigating Retrieval-Permutation-Induced Hallucinations in Retrieval-Augmented Generation](https://mlsanity.com/paper/2601.02993/) (2026)
- [ABCD: All Biases Come Disguised](https://mlsanity.com/paper/2602.17445/) (2026)
- [The Impossibility of Inverse Permutation Learning in Transformer Models](https://mlsanity.com/paper/2509.24125/) (2025)
- [Unexplored flaws in multiple-choice VQA make benchmarking unreliable](https://mlsanity.com/paper/2511.22341/) (2025)
- [Towards Order Fairness: Mitigating LLMs Order Sensitivity through Dual Group Advantage Optimization](https://mlsanity.com/paper/2605.11974/) (2026)
- [Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism](https://mlsanity.com/paper/2606.09484/) (2026)
- [Enhancing Tabular Learners with Context-Aware Semantic Embeddings](https://mlsanity.com/paper/2608.03565/) (2026)
- [Option-Order Randomisation Reveals a Distributional Position Attractor in Prompted Sandbagging](https://mlsanity.com/paper/2604.26206/) (2026)
- [GLM-RAG: Graph Language Models for Graph-Based Retrieval-Augmented Generation](https://mlsanity.com/paper/2607.28397/) (2026)
- [Counterfactual Benchmarking and Training for Factuality Consistency and Order-Robust Grounded Reasoning in LLMs over Heterogeneous Knowledge](https://mlsanity.com/paper/2608.07838/) (2026)
- [ufakzeka-karar: An Open Turkish Typed-Decision Model with Order-Invariant Option Scoring](https://mlsanity.com/paper/2610.06744/) (2026)

## Abstract (arXiv)

While large language models (LLMs) demonstrate impressive capabilities across numerous applications, their robustness remains a critical concern. This paper is motivated by a specific vulnerability: the order sensitivity of LLMs. This vulnerability manifests itself as the order bias observed when LLMs decide between possible options (for example, a preference for the first option) and the tendency of LLMs to provide different answers when options are reordered. The use cases for this scenario extend beyond the classical case of multiple-choice question answering to the use of LLMs as automated evaluators in AI pipelines, comparing output generated by different models. We introduce Set-LLM, a novel architectural adaptation for pretrained LLMs that enables the processing of mixed set-text inputs with permutation invariance guarantees. The adaptations involve a new attention mask and new positional encodings specifically designed for sets. We provide a theoretical proof of invariance and demonstrate through experiments that Set-LLM can be trained effectively, achieving comparable or improved performance and maintaining the runtime of the original model, while eliminating order sensitivity.