Algorithmic Thinking Theory
This foundational work offers a general perspective for understanding and improving reasoning in AI, potentially benefiting researchers and developers across the field.
The paper tackles the problem of analyzing reasoning algorithms in large language models by introducing a theoretical framework that formalizes iterative improvement and answer aggregation, providing a foundation for designing more powerful methods.
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan for generating and combining a set of solutions can be thought of as an algorithm for reasoning using a probabilistic oracle. We introduce a theoretical framework for analyzing such reasoning algorithms. This framework formalizes the principles underlying popular techniques for iterative improvement and answer aggregation, providing a foundation for designing a new generation of more powerful reasoning methods. Unlike approaches for understanding models that rely on architectural specifics, our model is grounded in experimental evidence. As a result, it offers a general perspective that may extend to a wide range of current and future reasoning oracles.