Algorithmic Thinking Theory

• URL: http://arxiv.org/abs/2512.04923v1
• Date: Thu, 04 Dec 2025 15:55:55 GMT
• Title: Algorithmic Thinking Theory
• Authors: MohammadHossein Bateni, Vincent Cohen-Addad, Yuzhou Gu, Silvio Lattanzi, Simon Meierhans, Christopher Mohri,
• Abstract summary: We introduce a theoretical framework for analyzing such reasoning algorithms.<n>Unlike approaches for understanding models that rely on architectural specifics, our model is grounded in experimental evidence.
• Score: 32.67988252212099
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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