Transformers Linearly Represent Highly Structured World Models
A recent study investigates how transformers build internal models while solving Sudoku puzzles. The research reveals that these models organize information based on the structure of the game rather than individual cells. Additionally, a specific circuit of neurons was identified that efficiently promotes the correct digit for a cell when only one option remains.
- ▪Transformers trained on Sudoku solving traces create a substructure world model.
- ▪The model organizes information around rows, columns, and boxes rather than individual cells.
- ▪A dedicated circuit of neurons detects when only one digit is possible for a specific cell.
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Computer Science > Machine Learning arXiv:2605.18847 (cs) [Submitted on 13 May 2026] Title:Transformers Linearly Represent Highly Structured World Models Authors:Roman Kniazev, Nathanaël Fijalkow View a PDF of the paper titled Transformers Linearly Represent Highly Structured World Models, by Roman Kniazev and 1 other authors View PDF HTML (experimental) Abstract:Do transformers, when trained on sequential reasoning traces, build internal models of the underlying task? And if so, does the structure of those internal representations mirror the structure of the domain? We train an 8-layer transformer on Sudoku solving traces and perform a mechanistic analysis of its internal computation. We establish two results.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
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