🤖 AI Summary
Existing AI agent architectures lack a unified mathematical foundation, hindering systematic comparison and principled design. Method: We propose a general modeling framework based on probabilistic chains, formally unifying prominent paradigms—including ReAct and multi-agent systems—as comparable stochastic processes. Central to our approach is the introduction of “degrees of freedom,” a quantitative measure characterizing adjustable dimensions in decision paths, information flow, and control structure across strategies. Contribution/Results: Through rigorous probabilistic formalization, the framework provides an abstract, unified description of agent behavior workflows, significantly improving both modeling accuracy and interpretability of success probability in complex tasks. It explicitly reveals design trade-offs and task-adaptation boundaries, thereby establishing a theoretical basis for architecture selection, analysis, and optimization.
📝 Abstract
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.