| title | Geometric Factual Recall in Transformers |
|---|---|
| authors | Shauli Ravfogel, Gilad Yehudai, Joan Bruna, Alberto Bietti |
| date | 2026-05-12 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2605.12426 |
| upvotes | 1 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf |
| abstract | How do transformer language models memorize factual associations? A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring parameter counts that scale linearly with the number of facts. We develop a theoretical and empirical account of an alternative, geometric form of memorization in which learned embeddings encode relational structure directly, and the MLP plays a qualitatively different role. In a controlled setting where a single-layer transformer must memorize random bijections from subjects to a shared attribute set, we prove that a logarithmic embedding dimension suffices: subject embeddings encode linear superpositions of their associated attribute vectors, and a small MLP acts as a relation-conditioned selector that extracts the relevant attribute via ReLU gating, and not as an associative key-value mapping. We extend these results to the multi-hop setting -- chains of relational queries such as ``Who is the mother of the wife of x?'' -- providing constructions with and without chain-of-thought that exhibit a provable capacity-depth tradeoff, complemented by a matching information-theoretic lower bound. Empirically, gradient descent discovers solutions with precisely the predicted structure. Once trained, the MLP transfers zero-shot to entirely new bijections when subject embeddings are appropriately re-initialized, revealing that it has learned a generic selection mechanism rather than memorized any particular set of facts. |
cite
@misc{ravfogel2026geometric,
title={Geometric Factual Recall in Transformers},
author={Shauli Ravfogel and Gilad Yehudai and Joan Bruna and Alberto Bietti},
year={2026},
eprint={2605.12426},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2605.12426}
}