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Humans have a powerful and mysterious capacity to reason. Working through aset of mental steps enables us to make inferences we would not be capable ofmaking directly even though we get no additional data from the world.Similarly, when large language models generate intermediate steps (a chain ofthought) before answering a question, they often produce better answers thanthey would directly. We investigate why and how chain-of-thought reasoning isuseful in language models, testing the hypothesis that reasoning is effectivewhen training data consists of overlapping local clusters of variables thatinfluence each other strongly. These training conditions enable the chaining ofaccurate local inferences to estimate relationships between variables that werenot seen together in training. We prove that there will exist a "reasoninggap", where reasoning through intermediate variables reduces bias, for thesimple case of an autoregressive density estimator trained on local samplesfrom a chain-structured probabilistic model. We then test our hypothesisexperimentally in more complex models, training an autoregressive languagemodel on samples from Bayes nets but only including a subset of variables ineach sample. We test language models' ability to match conditionalprobabilities with and without intermediate reasoning steps, finding thatintermediate steps are only helpful when the training data is locallystructured with respect to dependencies between variables. The combination oflocally structured observations and reasoning is much more data-efficient thantraining on all variables. Our results illustrate how the effectiveness ofreasoning step by step is rooted in the local statistical structure of thetraining data.

Why think step by step? Reasoning emerges from the locality of experience