# The Canonical Order Problem: When Large Language Models Are Unreliable Knowledge Bases for Multi-Valued Relations

arXiv: https://arxiv.org/abs/2609.36209 · HTML: https://mlsanity.com/paper/2609.36209/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [A Review on Language Models as Knowledge Bases](https://mlsanity.com/paper/2204.06031/) (2022)
- [Knowledge Graph-Guided Retrieval Augmented Generation](https://mlsanity.com/paper/2502.06864/) (2025)
- [Lost in Multilinguality: Dissecting Cross-lingual Factual Inconsistency in Transformer Language Models](https://mlsanity.com/paper/2504.04264/) (2025)
- [Do LLMs Really Adapt to Domains? An Ontology Learning Perspective](https://mlsanity.com/paper/2407.19998/) (2024)
- [OntoTune: Ontology-Driven Self-training for Aligning Large Language Models](https://mlsanity.com/paper/2502.05478/) (2025)
- [Extracting Multi-valued Relations from Language Models](https://mlsanity.com/paper/2307.03122/) (2023)
- [Explaining Caption-Image Interactions in CLIP Models with Second-Order Attributions](https://mlsanity.com/paper/2408.14153/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used as knowledge bases (KBs) due to the vast amount of knowledge they acquire during pre-training. While many works focus on extracting single relational triples, most real-world relations are multi-valued and require generating sets of entities. In this paper, we investigate how LLMs represent and generate multi-valued relations. We identify the canonical order problem: The probabilistic distributions inside LLMs organize many multi-valued relations according to a canonical ordering (e.g., alphabetical or chronological). Through mechanistic analysis, we show that set generation in LLMs can be thought of in terms of three phases: (1) retrieval of candidate entities, (2) internal sorting, and (3) selection of the next element. As a result, prompts aiming to construct KBs that deviate from this internal canonical ordering lead to a markedly reduced reliability of LLMs when aiming to generate complete sets for multi-valued relations.