Measuring the Unmeasurable: Markov Chain Reliability for LLM Agents

TL;DR

This paper introduces TraceToChain, a pipeline that models LLM agent traces as Markov chains, enabling detailed reliability analysis, diagnostics, and uncertainty quantification beyond traditional scalar metrics.

Contribution

It presents a reproducible method for fitting agent execution traces to Markov chains with diagnostics, uncertainty estimates, and a unified success-time distribution framework.

Findings

TraceToChain accurately fits agent traces with high goodness-of-fit.

The approach unifies various reliability metrics into a single success-time distribution.

Empirical tests show close alignment between fitted models and observed data.

Abstract

Large language model (LLM) agents increasingly operate as sequential software systems, but their reliability is often summarized by scalar benchmark metrics. Metrics such as pass$@k$, pass$^k$, and the reliability decay curve (RDC) are useful summaries, but they do not identify the success-time distribution being estimated, test whether traces support that distribution, or quantify finite-trace uncertainty. We present \textsc{TraceToChain}, a reproducible pipeline that fits agent execution traces to an absorbing discrete-time Markov chain (DTMC), $\hat M=(\hat Q,\hat R_\oplus,\hat R_\ominus)$, with explicit diagnostics and uncertainty. The pipeline builds an automatic cluster taxonomy, estimates transitions with Laplace-smoothed maximum-likelihood estimation (MLE), checks fit with a composite Akaike information criterion (AIC) and Kolmogorov--Smirnov (KS) goodness-of-fit certificate, and reports Dirichlet-posterior credible intervals and non-parametric bootstrap intervals. We adapt classical reliability mathematics (Kemeny--Snell~\cite{kemenysnell}, Cheung~\cite{cheung1980}, Goel--Okumoto~\cite{goelokt}) to agent traces. The resulting first-passage view reconciles metrics usually reported separately: pass$@k$, pass$^k$, and the RDC are projections of one success-time distribution. On seven controlled MAST-style frameworks with a strict 50/50 fit/test protocol, held-out empirical RDCs overlay their analytic counterparts with max $L_\infty^{\mathrm{RDC}} = 0.053$ (median $0.048$). A two-sample KS test on the first-passage cumulative distribution function (CDF) accepts the fitted chain with $p>0.05$ on $7/7$ frameworks (min $p = 0.78$), and per-entry $95\%$ posterior and bootstrap intervals agree to $\approx\!0.01$ at the median.