# Mathematical Framing for Different Agent Strategies

arXiv: https://arxiv.org/abs/2512.04469 · HTML: https://mlsanity.com/paper/2512.04469/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [The Prompt Report: A Systematic Survey of Prompt Engineering Techniques](https://mlsanity.com/paper/2406.06608/) (2024)
- [Reinforcement Learning for Improving Agent Design](https://mlsanity.com/paper/1810.03779/) (2018)
- [LLM-based Agentic Reasoning Frameworks: A Survey from Methods to Scenarios](https://mlsanity.com/paper/2508.17692/) (2025)
- [LLM-Powered AI Agent Systems and Their Applications in Industry](https://mlsanity.com/paper/2505.16120/) (2025)
- [Large language models for artificial general intelligence (AGI): A survey of foundational principles and approaches](https://mlsanity.com/paper/2501.03151/) (2025)

## Built on by (most cited first, 1 of 1)

- [Towards Discovery of Polymers for Insulin Delivery via Physics-Grounded Agentic Workflows](https://mlsanity.com/paper/2605.18831/) (2026)

## Abstract (arXiv)

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.