Parallelograms Strike Back: LLMs Generate Better Analogies than People

2026-03-19

AI Summary

This study investigates whether the classic “parallelogram” model of analogical reasoning is genuinely flawed or merely constrained by human limitations in generating relationally consistent analogies. By comparing human and large language model (LLM) performance on four-term analogy tasks—and integrating analyses of GloVe embedding geometry, human quality ratings, and lexical frequency statistics—the research demonstrates that LLM-generated analogies adhere more closely to the parallelogram structure and achieve higher overall quality. This advantage stems not from enhanced local semantic similarity but from superior relational consistency and more effective utilization of low-frequency vocabulary. The findings suggest that the parallelogram model remains valid; observed human underperformance primarily reflects cognitive constraints rather than inherent deficiencies in the model itself.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Four-term word analogies (A:B::C:D) are classically modeled geometrically as ''parallelograms,'' yet recent work suggests this model poorly captures how humans produce analogies, with simple local-similarity heuristics often providing a better account (Peterson et al., 2020). But does the parallelogram model fail because it is a bad model of analogical relations, or because people are not very good at generating relation-preserving analogies? We compared human and large language model (LLM) analogy completions on the same set of analogy problems from (Peterson et al., 2020). We find that LLM-generated analogies are reliably judged as better than human-generated ones, and are also more closely aligned with the parallelogram structure in a distributional embedding space (GloVe). Crucially, we show that the improvement over human analogies was driven by greater parallelogram alignment and reduced reliance on accessible words rather than enhanced sensitivity to local similarity. Moreover, the LLM advantage is driven not by uniformly superior responses by LLMs, but by humans producing a long tail of weak completions: when only modal (most frequent) responses by both systems are compared, the LLM advantage disappears. However, greater parallelogram alignment and lower word frequency continue to predict which LLM completions are rated higher than those of humans. Overall, these results suggest that the parallelogram model is not a poor account of word analogy. Rather, humans may often fail to produce completions that satisfy this relational constraint, whereas LLMs do so more consistently.

Problem

• word analogies
• parallelogram model
• large language models
• human analogy generation
• relational reasoning

Innovation

• parallelogram model
• large language models
• word analogies
• distributional semantics
• relational reasoning