# The Dichotomy Between Pattern Recognition and Step-by-Step Reasoning

arXiv: https://arxiv.org/abs/2610.09186 · HTML: https://mlsanity.com/paper/2610.09186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 13 of 13)

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- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Explore Theory of Mind: Program-guided adversarial data generation for theory of mind reasoning](https://mlsanity.com/paper/2412.12175/) (2024)
- [Transformers Can Represent n-gram Language Models](https://mlsanity.com/paper/2404.14994/) (2024)
- [A Theory of Learning with Autoregressive Chain of Thought](https://mlsanity.com/paper/2503.07932/) (2025)
- [Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space](https://mlsanity.com/paper/2605.12412/) (2026)
- [What Fits (Into Few Tokens) Doesn't Overfit: Compression and Generalization in ML Research Agents](https://mlsanity.com/paper/2606.11045/) (2026)
- [Do multimodal models imagine electric sheep?](https://mlsanity.com/paper/2605.09693/) (2026)

## Abstract (arXiv)

We argue that pattern recognition and step-by-step reasoning are two ends of a spectrum. A large language model (LLM) learns to reason step-by-step when data is structured such that the next token depends on a small amount of preceding context. Inference in LLMs resembles pattern recognition when the next token depends on a large amount of preceding context. If the next token depends on only the c most recent tokens, reasoning traces are paths on a De Bruijn graph whose nodes are c-length contexts and edges are next-token transitions between contexts. The set of reasoning traces of a task forms a directed acyclic subgraph of the De Bruijn graph. An LLM that has learned all edges of this subgraph can compose them to solve longer, unseen tasks, i.e., it reasons step-by-step. We prove that the number of edges is vanishingly small compared to the number of reasoning traces. Empirically, the number of training samples a transformer needs is a power law in the number of edges, so learning to reason step-by-step is sample efficient. We can induce De Bruijn structure in any task by maintaining a ``state'' that makes future reasoning independent of the past. The frequency of states in the reasoning trace determines c. We show, by fine-tuning Qwen2.5-1.5B-Instruct to solve equations and answer questions about stories, that frequent states (small c) result in higher accuracy but greater fragility to perturbations at test time. LLMs trained with a large c are only as good as models that perform pattern recognition without reasoning. A moderate density of states balances accuracy and robustness. We show that real-world data has De Bruijn structure: Qwen3-14B and Qwen3-32B retain over 75% of their accuracy on GSM8K, MATH-500 and GPQA-Diamond when attention is restricted to a sliding window less than 15% as long as the full reasoning trace.