Algorithmic Thinking Theory

TL;DR

This paper introduces a theoretical framework for analyzing iterative reasoning algorithms in large language models, formalizing principles behind techniques like solution improvement and answer aggregation to guide the development of more powerful reasoning methods.

Contribution

It provides a formal, experimentally grounded framework for understanding and designing iterative reasoning algorithms in LLMs, extending beyond specific model architectures.

Findings

Framework formalizes iterative reasoning principles

Supports design of more effective reasoning algorithms

Based on experimental evidence, not architecture specifics

Abstract

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.