Xuan-Bach Le

Phat T. Tran-Truong, Xuan-Bach Le

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.

Xuan-Bach Le, Dominik Wagner, Leon Witzman et al.

Linear temporal logic (LTL) and, more generally, $ω$-regular objectives are alternatives to the traditional discount sum and average reward objectives in reinforcement learning (RL), offering the advantage of greater comprehensibility and hence explainability. In this work, we study the relationship between these objectives. Our main result is that each RL problem for $ω$-regular objectives can be reduced to a limit-average reward problem in an optimality-preserving fashion, via (finite-memory) reward machines. Furthermore, we demonstrate the efficacy of this approach by showing that optimal policies for limit-average problems can be found asymptotically by solving a sequence of discount-sum problems approximately. Consequently, we resolve an open problem: optimal policies for LTL and $ω$-regular objectives can be learned asymptotically.

Hoang-Trung Nguyen, Tan-Minh Nguyen, Xuan-Bach Le et al.

This paper presents the methodologies and results of the NOWJ team's participation across all five tasks at the COLIEE 2025 competition, emphasizing advancements in the Legal Case Entailment task (Task 2). Our comprehensive approach systematically integrates pre-ranking models (BM25, BERT, monoT5), embedding-based semantic representations (BGE-m3, LLM2Vec), and advanced Large Language Models (Qwen-2, QwQ-32B, DeepSeek-V3) for summarization, relevance scoring, and contextual re-ranking. Specifically, in Task 2, our two-stage retrieval system combined lexical-semantic filtering with contextualized LLM analysis, achieving first place with an F1 score of 0.3195. Additionally, in other tasks--including Legal Case Retrieval, Statute Law Retrieval, Legal Textual Entailment, and Legal Judgment Prediction--we demonstrated robust performance through carefully engineered ensembles and effective prompt-based reasoning strategies. Our findings highlight the potential of hybrid models integrating traditional IR techniques with contemporary generative models, providing a valuable reference for future advancements in legal information processing.