Why think step by step? Reasoning emerges from the locality of experience (2304.03843v3)

Abstract: Humans have a powerful and mysterious capacity to reason. Working through a set of mental steps enables us to make inferences we would not be capable of making directly even though we get no additional data from the world. Similarly, when LLMs generate intermediate steps (a chain of thought) before answering a question, they often produce better answers than they would directly. We investigate why and how chain-of-thought reasoning is useful in LLMs, testing the hypothesis that reasoning is effective when training data consists of overlapping local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables reduces bias, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis experimentally in more complex models, training an autoregressive LLM on samples from Bayes nets but only including a subset of variables in each sample. We test LLMs' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables. The combination of locally structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Overview

In an intriguing paper unfolding from Stanford University, researchers explore the mechanics of reasoning. They probe into why stringing together a series of inferences—akin to reasoning through steps—can enhance our understanding and lead to better decisions, despite the absence of additional data. The paper scrutinizes the efficacy of reasoning in understanding the world around us and resolves whether similar processes enhance the performance of LLMs.

The Hypothesis

At the core of the paper lies a hypothesis: reasoning in LLMs is potent when the training involves data that clusters around local, strongly interrelated variables. This mirrors human cognition, where experiences are often confined to the immediate surroundings yet inform decisions impacting distant objectives. The paper postulates that LLMs, quite similarly, are fed on text data redolent with adjacent themes and are thus adept at processing closely tied concepts. However, when making leaps between less frequently paired information, LLMs and humans alike benefit from delineating a pathway through associated deductive steps.

Mathematical Insights

The paper doesn’t simply assert intuitions; it steepens its hypothesis in mathematical rigor. For the analytically inclined, it proves a "reasoning gap" through the lens of autoregressive density estimators—a class of statistical models. In essence, reasoning through a chain of intermediate variables minimizes estimation bias, a finding illuminated by a formal proof in the context of a simplified Bayes' net structure. Supplementing this proof are controlled experiments using synthetic datasets to emulate local structures, which confirmed that intermediate reasoning indeed bridges gaps in data relationships not directly observable in training.

Real-world Implications and Conclusion

What does all this mean in practical terms? The research projects illuminating real-world implications for AI development. Constructing data-driven models that reflect the 'locality' principle akin to clustering of human experiences could enable AI to reason with increased deftness, similar to a human navigating through a complex thought process. Experimentally, such AI models are shown to match conditional probabilities more accurately, embodying a form of efficiency that could catalyze significant advancements in understanding and fostering reasoning in artificial intelligence. This exploration charts a path for future inquiries into the fusion of local observations, reasoned AI responses, and efficient AI training, remarkably informing the cognitive emulation landscape within the AI sphere.