Algorithmic Thinking Theory
On the map: LLM reasoning → Reasoning benchmarks and evaluation
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 1 of its 21 references that are in the map. First posted on arXiv 4 Dec 2025.
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References · 1
- 2024The Complexity Dynamics of Grokkingcited by 22
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- 2026The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes
- 2024Distilling Algorithmic Reasoning from LLMs via Explaining Solution Programs
- 2024Aggregation of Reasoning: A Hierarchical Framework for Enhancing Answer Selection in Large Language Models
- 2023Algorithm of Thoughts: Enhancing Exploration of Ideas in Large Language Models
- 2022Towards Reasoning in Large Language Models: A Survey
- 2025Advancing Reasoning in Large Language Models: Promising Methods and Approaches
- 2024LLM Reasoners: New Evaluation, Library, and Analysis of Step-by-Step Reasoning with Large Language Models
- 2025PEA: Enhancing LLM Performance on Computational-Reasoning Tasks