Understanding Agent Scaling in LLM-Based Multi-Agent Systems via Diversity

TL;DR

This work addresses why simply increasing the number of homogeneous agents in LLM-based MAS yields diminishing returns and how diversity can overcome this limit. It introduces an information-theoretic framework where performance is bounded by the intrinsic task uncertainty $H(Y|X)$ and governed by the number of effective channels $K$ and a complementarity rate $\alpha$, with a practical proxy $K^*$ to measure channel diversity without ground-truth labels. The authors show that homogeneous ensembles saturate early due to high output correlation, while heterogeneous ensembles create complementary channels that yield fast-then-slow information gains following the shape $1-e^{-\alpha K}$; empirically, 2 diverse agents can match or exceed 16 homogeneous agents across tasks. They validate the theory on Vote and Debate MAS workflows over seven benchmarks, linking $K^*$ to accuracy and providing design guidelines that favor diversity-aware configurations and targeted improvements to correct-path reasoning diversity. Overall, the paper offers principled, architecture-agnostic bounds and a practical metric for engineering robust, efficient MAS through diversity, rather than brute compute scaling.

Abstract

LLM-based multi-agent systems (MAS) have emerged as a promising approach to tackle complex tasks that are difficult for individual LLMs. A natural strategy is to scale performance by increasing the number of agents; however, we find that such scaling exhibits strong diminishing returns in homogeneous settings, while introducing heterogeneity (e.g., different models, prompts, or tools) continues to yield substantial gains. This raises a fundamental question: what limits scaling, and why does diversity help? We present an information-theoretic framework showing that MAS performance is bounded by the intrinsic task uncertainty, not by agent count. We derive architecture-agnostic bounds demonstrating that improvements depend on how many effective channels the system accesses. Homogeneous agents saturate early because their outputs are strongly correlated, whereas heterogeneous agents contribute complementary evidence. We further introduce $K^*$, an effective channel count that quantifies the number of effective channels without ground-truth labels. Empirically, we show that heterogeneous configurations consistently outperform homogeneous scaling: 2 diverse agents can match or exceed the performance of 16 homogeneous agents. Our results provide principled guidelines for building efficient and robust MAS through diversity-aware design. Code and Dataset are available at the link: https://github.com/SafeRL-Lab/Agent-Scaling.

Figures (8)

• Figure 1: Effect of model diversity. We compare a mixture of three LLMs (Qwen-2.5-7B, Llama-3.1-8B, Mistral-7B) with the average of independent single-LLM runs.
• Figure 2: Scaling behavior of homogeneous multi-agent voting. Success rate versus agent count N on seven tasks for three base models. Performance improves with N but saturates, indicating clear diminishing marginal gains at larger agent counts.
• Figure 3: A comparison between homogeneous and heterogeneous systems. In a homogeneous system, agents with identical configurations result in redundant behavior and limited information coverage. In contrast, heterogeneous agents, through diverse configurations (e.g., varying models or personas), provide complementary coverage and better diversity in the information processed, allowing for more effective problem-solving across different workflows.
• Figure 4: Diversity analysis of the Vote and Debate mechanisms across all datasets. Each subfigure corresponds to one dataset and visualizes absolute performance as a $4 \times 5$ heatmap, where rows represent progressively enriched diversity layers (L1--L4) and columns denote the number of agents $N$. Colors indicate success rate values: cyan (lowest) to red (highest).
• Figure 5: Correlation between cosine similarity and success rate. Homogeneous settings show higher similarity but lower performance; heterogeneous personas preserve diversity and improve accuracy.

Theorems & Definitions (35)

• Definition 3.1: LLM-based Multi-Agent System
• Theorem 3.2: Finite Information Budget
• Definition 3.3: Agent Configuration Type
• Definition 4.1: Complementarity Rate
• Definition 4.2: Effective Channel Representation
• Theorem 4.3: Geometric Contraction with Effective Channels
• Corollary 4.4: Heterogeneity Advantage
• Definition 1.1: Conditional Mutual Information
• Lemma 1.2: Chain Rule for Mutual Information
• Lemma 1.3: Data Processing Inequality