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

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.

Large language models (LLMs) have achieved strong performance on text-to-knowledge graph generation and related tasks. Nevertheless, it is still unclear whether they accurately model the direction-dependent semantics of inverse relations, in which reversing the order of the arguments alters the meaning of a relation (e.g., mother versus child). To the best of our knowledge, this work presents the first systematic study of inverse relation directionality in LLMs, using a benchmark consisting of 5,457 instances spanning 27 distinct inverse relation labels. We evaluate five open-source LLMs under a multiple-choice prompting framework and further examine the influence of relation descriptions and entity representations by substituting the original entities with synthetic and masked entities. Our findings reveal systematic asymmetries in inverse relation classification across LLMs, indicate that relation descriptions do not consistently improve performance, and show that model performance can be sensitive to variations in entity representations.

Large language models (LLMs) have increasingly supported response generation grounded in user-provided knowledge spanning heterogeneous structures. However, existing benchmarks provide limited assessment of whether LLMs can faithfully perform multi-hop reasoning chains across such knowledge contexts while remaining robust to variations in their input order. We introduce TKFQA, a factuality consistency benchmark comprising 10,130 question-answering (QA) pairs grounded in tables, texts, and knowledge graphs (KGs). Each example is constructed from an explicit counterfactual reasoning chain, enabling the joint evaluation of answer correctness, reasoning-chain accuracy, and robustness to different input-order. An extensive evaluation of 14 open- and closed-source LLMs reveals that state-of-the-art models exhibit limited reasoning-chain accuracy and remain sensitive to variations in the input order of heterogeneous knowledge contexts. To address these limitations, we propose ORLF, an LLM-agnostic training framework that models cross-context topological relations through knowledge-specific latent vectors. ORLF integrates context-wise position encoding, a latent-bridge attention mask, and topological knowledge bias to preserve knowledge-specific bias and encode topological semantics. Experiments across four LLM backbones show that ORLF outperforms competitive training-free and LoRA-based baselines, improving average Exact Match and Reasoning-Chain Accuracy by 2.15% and 4.29%, respectively, while reducing order-induced performance standard deviation by 0.04% to 3.01%.