Asymmetricity: A Benchmark for Evaluating LLMs on Symmetric and Asymmetric Relation Understanding

Asymmetricity is a benchmark dataset designed to evaluate large language models (LLMs) on their ability to distinguish and reason over symmetric (e.g., borders) and antisymmetric (e.g., parent of) relations in natural language. The dataset is derived from Wikidata triples and cast into a natural language inference (NLI) format, enabling fine-grained analysis of relational understanding.

The dataset includes a variety of textual forms—both in natural language and in a delexicalized version where entities are replaced by Wikidata IDs (e.g., Q7024230). This enables models to be evaluated both on surface-level text and on abstract relational structure.

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Overview

Understanding the symmetry properties of relations is essential for robust reasoning. For example, if A is the parent of B, then B is the parent of A should clearly be false. Many LLMs, however, struggle to consistently apply this logic, particularly when the phrasing or entity names change.

The Asymmetricity dataset provides a structured and scalable testbed for evaluating this capability, drawing on real-world knowledge base relations and reformulating them as NLI-style sentence pairs.

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Motivation

Current language models often rely on surface patterns and statistical co-occurrence, which can obscure their understanding of logical constraints like symmetry and directionality. This benchmark tests models on:

• Recognizing whether a relation is symmetric or asymmetric
• Identifying correct entailments and contradictions in natural language
• Generalizing across entity names and abstract identifiers (Wikidata IDs)

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Dataset Design

Each example is based on a Wikidata triple involving two entities and a relation. The data is converted into a natural language premise and a hypothesis representing either the same or reversed triple. A label indicates whether the hypothesis logically follows from the premise.

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Splits:

• https://huggingface.co/datasets/MoyYuan/Asymmetricity-Text
• https://huggingface.co/datasets/MoyYuan/Asymmetricity-Text-NLI
• https://huggingface.co/datasets/MoyYuan/Asymmetricity-Delex
• https://huggingface.co/datasets/MoyYuan/Asymmetricity-Delex-NLI

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Data variants include:

• *_text.json: Premise and hypothesis expressed using natural language names for entities.
• *_delex_text.json: Premise and hypothesis using Wikidata IDs instead of surface names (e.g., Q5, Q42).
• *_nli.json: Reformatted for compatibility with natural language inference classifiers.

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Evaluation Focus

This dataset supports research in:

• Logical consistency and relation reasoning in LLMs
• Sensitivity to relation directionality and symmetry
• Robustness across lexicalized and abstract (ID-based) inputs
• Pretraining biases related to relation semantics

It is suitable for prompting, zero/few-shot evaluation, embedding-based retrieval, and supervised fine-tuning.

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Data Format

Each line in the dataset is a JSON object with fields:

• premise: Natural language sentence expressing a relation between two entities
• hypothesis: Variant of the premise sentence with the entity order possibly reversed
• label: Either entailment or contradiction, depending on whether the relation is symmetric or not
• relation: The original Wikidata property ID (e.g., P40)
• entity_a, entity_b: Entity identifiers or names used in the sentence
• delexicalized: Boolean indicating whether the sentence uses Wikidata IDs instead of entity names

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Citation

If you use this dataset in your work, please cite the following paper:

@article{yuan2025capturing,
  title={Capturing Symmetry and Antisymmetry in Language Models through Symmetry-Aware Training Objectives},
  author={Yuan, Zhangdie and Vlachos, Andreas},
  journal={arXiv preprint arXiv:2504.16312},
  year={2025}
}

Intended Use

The dataset is intended for academic research and educational use. It is particularly useful for probing relational understanding in language models and for developing systems that reason over structured knowledge in textual form.

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Ethical Considerations

• Bias and Representation: Some relations may reflect cultural or societal norms encoded in Wikidata. Users should be cautious in interpreting model behavior around such relations.
• Interpretability: Inference about relations is abstract and often subtle. Human evaluation may be needed to interpret model predictions accurately.
• Misuse Risk: This dataset is not designed for high-stakes reasoning applications. It is intended to support the development and evaluation of models in controlled research settings.