Position: Scaling LLM Agents Requires Asymptotic Analysis with LLM Primitives

2025-02-04

AI Summary

Existing task decomposition methods in LLM-based multi-agent systems lack rigorous theoretical foundations, relying instead on heuristic, intuition-driven role assignments. Method: This paper introduces the first asymptotic complexity analysis framework for LLM multi-agent systems, treating LLM forward passes as atomic computational primitives. By abstracting away internal model architecture, it models computational cost as an asymptotic function of the number of forward passes, unifying the analysis of task decomposition, agent coordination, and reasoning depth. Contribution/Results: The framework establishes a new paradigm for evaluating LLM agent efficiency, enabling provably efficient decomposition strategies and scalable collaborative architectures. It provides both theoretical grounding and concrete optimization pathways for system design—formally characterizing how decomposition granularity, agent interaction patterns, and inference depth jointly govern asymptotic scalability. This bridges a critical gap between empirical multi-agent engineering and principled computational complexity theory in LLM systems.

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Decomposing hard problems into subproblems often makes them easier and more efficient to solve. With large language models (LLMs) crossing critical reliability thresholds for a growing slate of capabilities, there is an increasing effort to decompose systems into sets of LLM-based agents, each of whom can be delegated sub-tasks. However, this decomposition (even when automated) is often intuitive, e.g., based on how a human might assign roles to members of a human team. How close are these role decompositions to optimal? This position paper argues that asymptotic analysis with LLM primitives is needed to reason about the efficiency of such decomposed systems, and that insights from such analysis will unlock opportunities for scaling them. By treating the LLM forward pass as the atomic unit of computational cost, one can separate out the (often opaque) inner workings of a particular LLM from the inherent efficiency of how a set of LLMs are orchestrated to solve hard problems. In other words, if we want to scale the deployment of LLMs to the limit, instead of anthropomorphizing LLMs, asymptotic analysis with LLM primitives should be used to reason about and develop more powerful decompositions of large problems into LLM agents.

Problem

• Scaling LLM agents efficiently
• Optimal decomposition of hard problems
• Asymptotic analysis with LLM primitives

Innovation

• Decompose problems into LLM agents
• Use asymptotic analysis for efficiency
• Treat LLM forward pass as cost unit