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

Amrut Nadgir, Pratik Chaudhari, Vijay Balasubramanian

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…