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

Timo Pierre Schrader; Annemarie Friedrich; Simon Razniewski; Lukas Lange

cs.CLSep 28, 2026

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

Authors: Timo Pierre Schrader, Annemarie Friedrich, Simon Razniewski, Lukas Lange

Organizations: University of Augsburg, Augsburg, Germany · ScaDS.AI & TU Dresden, Dresden, Germany · Bosch Center for Artificial Intelligence, Renningen, Germany

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Precision-recall curves for LLM set generation across 37 topics. We compare four distinct settings: $\displaystyle\bullet$ without any examples; $\displaystyle\blacksquare$ with the first element in canonical order; $\displaystyle\square$ with a single random element; and $\displaystyle\triangle$ with randomly shuffled elements. Providing the first element as an example always achieves the best results.

Panel of Figure 2 — Figure 2: Example demonstrating a multi-valued relation in a KB. The dependent nodes share the same head node and are connected to it via the same relation type.

Topic	Count $\displaystyle\downarrow$	Ordering	Size
Nobel prize categories	6	other	small
Ancient wonders	7	chronological	small
Newton spectrum colors	7	numerical	small
Crystal systems	7	other	small
Seven seas	7	other	small
Moon phases	8	chronological	small

Table 1: The 37 distinct topics in our dataset along with their number of entities

\displaystyle\mid\mathcal{S}(t)\mid

, type of canonical ordering, and categorization into the three set sizes.

12B

27B

Example(s)

0-shot

\displaystyle 56.9

\displaystyle 36.2

\displaystyle 36.3

\displaystyle 78.7

\displaystyle 79.1

\displaystyle 50.2

92.5

89.7

\displaystyle 80.9

\displaystyle 86.4

\displaystyle 88.4

85.1

First

61.3

51.8

36.4

84.7

85.5

66.2

\displaystyle 92.2

\displaystyle 87.4

82.6

89.7

89.9

\displaystyle 83.4

1 Random

\displaystyle 53.0

\displaystyle 46.8

\displaystyle 24.6

\displaystyle 77.5

\displaystyle 74.7

\displaystyle 49.6

\displaystyle 90.1

\displaystyle 83.3

\displaystyle 72.8

\displaystyle 88.6

\displaystyle 87.7

\displaystyle 81.6

\displaystyle k

Random

\displaystyle 42.2

\displaystyle 34.7

\displaystyle 13.0

\displaystyle 69.1

\displaystyle 58.3

\displaystyle 34.6

\displaystyle 84.7

\displaystyle 73.9

\displaystyle 48.2

\displaystyle 83.9

\displaystyle 77.9

\displaystyle 57.5

Table 2: Average F1 (%) for models in the Gemma-3 family, split by set sizes and prefix strategy. S = small, R = regular, L = large.

LLM Reliability

Large language model reliability studies whether outputs remain correct, calibrated, robust, and controllable across prompts, contexts, and deployment conditions.

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The Geometry of Contextual Relations: Language Models Address Facts by Order of Mention

Yufa Zhou

Duke University

In-Context Retrieval Factual Knowledge in Language Models Representation Geometry in Language Models Factual QA

Open paper AskPDF arXiv

Human reasoning depends on how objects are related within propositions. How do relations organize the language representations of contextual contents? We give an LLM a list of facts in its context (e.g., Alice eats an apple. Bob eats a pear.) and measure how its hidden state changes when the question switches from what Alice eats to what Bob eats. Averaged over many lists, this change is a steering vector, which we call the ordinal vector. It points to a fact by its order of mention, the order in which the facts were stated in the context. We find that LLMs represent the fact a question asks about by its order of mention, not by the name the question contains. We state this as the ordinal addressing hypothesis: each order of mention has a fact address in the model's state, shared by all contexts, and a question moves the state to the fact address of the fact it asks about, while the context supplies what that fact says. Across Qwen, Gemma, and Llama, fact addresses are (1) ordered by mention: query states are organized by the order of facts, not of names, even when one fact has multiple subjects; (2) steerable: added to a question about the first fact of a new list, the ordinal vector makes the model answer with the second fact of that list; (3) low-rank: they span a low-rank subspace in which the first-mentioned fact is the easiest to reach, surprisingly similar to human recall; and (4) emergent: they are shared in late-middle layers, hold from 1.5B to 32B parameters, and form early in pretraining. Language models reach a stated fact by where it was mentioned, deepening our understanding of LLM reasoning.

Abstract

LLM Reliability

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