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

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite that fact that we get no additional data from the world. Similarly, large language models can perform better at complex tasks through chain-of-thought reasoning, where they generate intermediate steps before answering a question. We use language models to investigate the questions of when and why reasoning is helpful, testing the hypothesis that reasoning is effective when training data consisting of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We train an autoregressive transformer on samples from joint distributions defined by Bayes nets, but only include a subset of all the variables in each sample. We compare language models' ability to match conditional probabilities both with and without intermediate reasoning steps, finding that intermediate steps help only when the training data is locally structured with respect to dependencies between variables. Furthermore, intermediate variables need to be relevant to the relationship between observed information and target inferences. Our results illustrate how the statistical structure of training data drives the effectiveness of reasoning step by step.