---
title: "Causal Language Modeling Can Elicit Search and Reasoning"
description: "The authors build human-style solvers that never backtrack. 56 references, cited by 11 papers here."
authors: ["Kulin Shah", "Nishanth Dikkala", "Xin Wang", "Rina Panigrahy"]
year: 2024
venue: "arXiv:2409.10502"
source: "https://arxiv.org/abs/2409.10502"
doi: "10.48550/arxiv.2409.10502"
arxiv: "2409.10502"
licence: "CC BY-SA 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by-sa/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/shah-2024-causal-language-modeling-elicit-search/"
---
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# Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles

**Authors:** Kulin Shah, [Nishanth Dikkala](https://md.research.elamur.ai/free/en/authors/nishanth-dikkala/), [Xin Wang](https://md.research.elamur.ai/free/en/authors/xin-wang/) and Rina Panigrahy · **Year:** 2024 · **Venue:** [arXiv:2409.10502](https://md.research.elamur.ai/free/en/venues/neural-information-processing-systems/) ([NeurIPS 2024](https://md.research.elamur.ai/free/en/venues/neural-information-processing-systems/2024/)) · **Licence:** [CC BY-SA 4.0 (arXiv)](http://creativecommons.org/licenses/by-sa/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2409.10502) · [PDF](https://arxiv.org/pdf/2409.10502) · [DOI 10.48550/arxiv.2409.10502](https://doi.org/10.48550/arxiv.2409.10502) · [arXiv 2409.10502](https://arxiv.org/abs/2409.10502) · [OpenAlex](https://openalex.org/W4415797573)

**Citations:** 1 citations (OpenAlex, 2026-10-14) · [11](https://md.research.elamur.ai/free/en/papers/shah-2024-causal-language-modeling-elicit-search/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper examines whether Transformers trained only with next-token prediction can learn real search and reasoning, using Sudoku and Zebra (Einstein) logic puzzles as controlled synthetic tasks. The authors build human-style solvers that never backtrack. The Sudoku solver uses 7 common strategies, and the Zebra solver adds clues until a puzzle becomes solvable. Each puzzle is posed as a sequence-to-sequence problem. Models are trained from scratch with the answer cells in one of three orders: fixed (left to right), random, or the order in which the solver fills them. The solver order works as Chain-of-Thought supervision.

Training on solver order is decisive. Fixed or random orders mostly fail, while solver-ordered training with beam search solves about 94% of Sudokus and 92% of Zebra puzzles. Linear probes show that the model's activations encode the set of candidate values for every empty cell. This matters for the debate on LLM reasoning: suitably decomposed training data, without full search traces, can give a capable implicit reasoning engine.

## Key points
- **Data:**
  - About 1.9M Sudoku puzzles taken from [Rad20], kept only if the 7-strategy solver can finish them.
  - About 320k symbolic Zebra puzzles, 20k for each size from (3,3) to (6,6), with 15k held out for evaluation.
- **Sudoku results:**
  - Fixed-order training gives 58.64% cell accuracy but only 7.2% fully solved puzzles.
  - Solver-order training reaches 87.18% fully solved.
  - Beam search raises this to 91.36% with width 3 and 94.21% with width 5.
- **Where the difficulty lies:** When the solver supplies the next cell position, cell accuracy rises to 99.02%. This shows that choosing which cell to fill is harder than computing its value.
- **Zebra results:**
  - Solver order gives 91.17% fully solved (95.63% cell accuracy), rising to 92.04% with beam width 5.
  - Fixed order gives 79.36%, and random order is close to 0%.
- **Baselines and probing:**
  - With 4-shot CoT prompting on 3000 Sudokus, GPT-4o and Gemini-1.5 Pro solved 0% of puzzles, with roughly 10% of cells correct.
  - Linear probing recovers per-cell candidate sets, even though candidates were never supervised.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

📚 Shelves (2): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works

🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 4,145 works · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,948 works

## Cite

Cite as: Kulin Shah, Nishanth Dikkala, Xin Wang and Rina Panigrahy. 2024. Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles. arXiv:2409.10502.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{shah2024causal,
  title = {{Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles}},
  author = {Kulin Shah, Nishanth Dikkala, Xin Wang and Rina Panigrahy},
  year = {2024},
  doi = {10.48550/arxiv.2409.10502},
  eprint = {2409.10502},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2409.10502}
}
```

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*Updated 3 November 2026*