Parallelograms Strike Back: When AI Outperforms Humans at Generating Analogies

*An accessible walkthrough of the paper "Parallelograms Strike Back: LLMs Generate Better Analogies than People" (Liu, Marjieh, Zhu, Goldberg & Griffiths, arXiv:2603.19066), from Princeton University and the University of Hong Kong.*

The classic puzzle

Consider the four-term analogy A:B::C:D — *king is to queen as man is to ______?* The answer, of course, is "woman." This simple task rests on analogical reasoning, a cornerstone of human cognition emphasized by thinkers from Aristotle to Einstein.

Key points

• The parallelogram model (1973). Rumelhart and Abrahamson proposed that concepts live in a geometric space and relations are vectors: solving A:B::C:? means completing a parallelogram, i.e., vector(D) ≈ vector(C) + (vector(B) - vector(A)).
• word2vec revival (2013). Mikolov et al.'s word embeddings famously satisfied equations like vector("king") - vector("man") + vector("woman") ≈ vector("queen"), seemingly validating the model.
• The 2020 challenge. Peterson, Smith & Griffiths showed the parallelogram model predicted *human* answers poorly; a simple C:D similarity heuristic ("pick the word most similar to C") fit better. This was read as evidence the model itself was wrong.

The new experiment

The authors considered two explanations:

• A: the model is wrong — human analogy-making isn't geometric.
• B: humans underperform — time pressure, cognitive load, and knowledge limits keep people from producing model-consistent answers.

To discriminate, they reused Peterson's analogy items, had six frontier LLMs (GPT-4, Claude, etc.) answer them, and recruited human judges to blindly compare human vs. LLM answers.

Findings

• LLMs won the blind comparison. Human judges consistently rated LLM-generated analogies as better than human-generated ones — a statistically significant result across all tested models.
• The parallelogram strikes back. LLM answers showed higher parallelogram alignment in GloVe embedding space than human answers, supporting explanation B: the model is valid; humans just don't follow it well.
• Why LLMs win:
• They avoid the availability bias that leads humans to pick common, easily retrieved words that fit local similarity but not relational structure.
• They avoid humans' long tail of poor, irrelevant answers. On the modal (most common) answers, humans and LLMs perform similarly — the gap comes from the tail.
• Rule comparison. For human answers, the C:D similarity heuristic beat the parallelogram model (replicating 2020). For LLM answers, all three tested rules (parallelogram, C:D similarity, nearest neighbor) fit better, and the gap between the parallelogram model and the similarity heuristic shrank by more than half (from 27,264 to 13,355 ranking positions).
• What predicts quality: higher parallelogram alignment (positive, significant) and lower word frequency (positive effect for less common words, significant) predicted analogies judged better; local similarity sensitivity did not.

Implications

• Reassessing human analogy ability. A model's failure to fit human behavior may reflect human performance limits (fatigue, shortcuts, time pressure) rather than a wrong theory — like someone answering "5" to "2+2?" under pressure.
• LLMs as idealized cognitive models. Free of cognitive load, retrieval failures, and knowledge limits, LLMs offer a reference point for how analogy *could* work, helping separate human-specific constraints from the underlying computation.
• Geometry and meaning. The success of vector-space geometry in capturing relational structure reopens questions about whether semantics can be fully geometric.
• Applications. Better AI analogy generators for education and creativity training, explicit geometric constraints in neural models, and LLMs as new tools for testing cognitive theories.

References

1. Liu, Q. E., Marjieh, R., Zhu, J.-Q., Goldberg, A. E., & Griffiths, T. L. (2026). *Parallelograms Strike Back: LLMs Generate Better Analogies than People.* arXiv:2603.19066. 2. Peterson, J. C., Smith, K. A., & Griffiths, T. L. (2020). *Evaluating Vector-Space Models of Analogy.* Proceedings of the 42nd Annual Meeting of the Cognitive Science Society. 3. Rumelhart, D. E., & Abrahamson, A. A. (1973). *A Model for Analogical Reasoning.* Cognitive Psychology, 5(1), 1–28. 4. Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013). *Efficient Estimation of Word Representations in Vector Space.* arXiv:1301.3781. 5. Pennington, J., Socher, R., & Manning, C. D. (2014). *GloVe: Global Vectors for Word Representation.* EMNLP 2014, 1532–1543.

*This is a popular-science explainer; for precise details, consult the original paper.*