Information Fidelity in Tool-Using LLM Agents: A Martingale Analysis of the Model Context Protocol

TL;DR

This paper presents a theoretical framework analyzing how errors propagate in LLM-based tool-using agents, demonstrating linear growth and bounded deviations, validated by experiments across multiple models, with practical guidelines for reliable system deployment.

Contribution

It introduces the first formal analysis of error accumulation in Model Context Protocol agents, establishing concentration bounds and validating them empirically across various LLMs.

Findings

Error growth is linear over time.

Semantic weighting reduces distortion by 80%.

Periodic re-grounding every 9 steps effectively controls errors.

Abstract

As AI agents powered by large language models (LLMs) increasingly use external tools for high-stakes decisions, a critical reliability question arises: how do errors propagate across sequential tool calls? We introduce the first theoretical framework for analyzing error accumulation in Model Context Protocol (MCP) agents, proving that cumulative distortion exhibits linear growth and high-probability deviations bounded by $O(\sqrt{T})$. This concentration property ensures predictable system behavior and rules out exponential failure modes. We develop a hybrid distortion metric combining discrete fact matching with continuous semantic similarity, then establish martingale concentration bounds on error propagation through sequential tool interactions. Experiments across Qwen2-7B, Llama-3-8B, and Mistral-7B validate our theoretical predictions, showing empirical distortion tracks the linear trend with deviations consistently within $O(\sqrt{T})$ envelopes. Key findings include: semantic weighting reduces distortion by 80\%, and periodic re-grounding approximately every 9 steps suffices for error control. We translate these concentration guarantees into actionable deployment principles for trustworthy agent systems.