The repetition problem, where Large Language Models (LLMs) continuously generate repetitive content without proper termination, poses a critical challenge in production deployments, causing severe performance degradation and system stalling. This paper presents a comprehensive investigation and multiple practical solutions for the repetition problem encountered in real-world batch code interpretation tasks. We identify three distinct repetition patterns: (1) business rule generation repetition, (2) method call relationship analysis repetition, and (3) PlantUML diagram syntax generation repetition. Through rigorous theoretical analysis based on Markov models, we establish that the root cause lies in greedy decoding's inability to escape repetitive loops, exacerbated by self-reinforcement effects. Our comprehensive experimental evaluation demonstrates three viable solutions: (1) Beam Search decoding with early_stopping=True serves as a universal post-hoc mechanism that effectively resolves all three repetition patterns; (2) presence_penalty hyperparameter provides an effective solution specifically for BadCase 1; and (3) Direct Preference Optimization (DPO) fine-tuning offers a universal model-level solution for all three BadCases. The primary value of this work lies in combining first-hand production experience with extensive experimental validation. Our main contributions include systematic theoretical analysis of repetition mechanisms, comprehensive evaluation of multiple solutions with task-specific applicability mapping, identification of early_stopping as the critical parameter for Beam Search effectiveness, and practical production-ready solutions validated in real deployment environments.

Contemporary DevSecOps pipelines have to deal with the evolution of security in an ever-continuously integrated and deployed environment. Existing methods,such as rule-based intrusion detection and static vulnerability scanning, are inadequate and unreceptive to changes in the system, causing longer response times and organization needs exposure to emerging attack vectors. In light of the previous constraints, we introduce AutoGuard to the DevSecOps ecosystem, a reinforcement learning (RL)-powered self-healing security framework built to pre-emptively protect DevSecOps environments. AutoGuard is a self-securing security environment that continuously observes pipeline activities for potential anomalies while preemptively remediating the environment. The model observes and reacts based on a policy that is continually learned dynamically over time. The RL agent improves each action over time through reward-based learning aimed at improving the agent's ability to prevent, detect and respond to a security incident in real-time. Testing using simulated ContinuousIntegration / Continuous Deployment (CI/CD) environments showed AutoGuard to successfully improve threat detection accuracy by 22%, reduce mean time torecovery (MTTR) for incidents by 38% and increase overall resilience to incidents as compared to traditional methods. Keywords- DevSecOps, Reinforcement Learning, Self- Healing Security, Continuous Integration, Automated Threat Mitigation

Real-world tasks and environments exhibit differences from the static datasets that large language models (LLMs) are typically evaluated on. Such tasks can involve sequential interaction, requiring coherent updating of beliefs in light of new evidence, and making appropriate decisions based on those beliefs. Predicting how LLMs will perform in such dynamic environments is important, but can be tricky to determine from measurements in static settings. In this work, we examine two critical components of LLM performance: the ability of LLMs to coherently update their beliefs, and the extent to which the actions they take are consistent with those beliefs. First, we find that LLMs are largely inconsistent in how they update their beliefs; models can exhibit up to a 30% average difference between the directly elicited posterior, and the correct update of their prior. Second, we find that LLMs also often take actions which are inconsistent with the beliefs they hold. On a betting market, for example, LLMs often do not even bet in the same direction as their internally held beliefs over the underlying outcomes. We also find they have moderate self-inconsistency in how they respond to challenges by users to given answers. Finally, we show that the above properties hold even for strong models that obtain high accuracy or that are well-calibrated on the tasks at hand. Our results highlight the difficulties of predicting LLM behavior in complex real-world settings.

This article presents the first systematic review of unsupervised and semi-supervised computational text-based ideal point estimation (CT-IPE) algorithms, methods designed to infer latent political positions from textual data. These algorithms are widely used in political science, communication, computational social science, and computer science to estimate ideological preferences from parliamentary speeches, party manifestos, and social media. Over the past two decades, their development has closely followed broader NLP trends -- beginning with word-frequency models and most recently turning to large language models (LLMs). While this trajectory has greatly expanded the methodological toolkit, it has also produced a fragmented field that lacks systematic comparison and clear guidance for applied use. To address this gap, we identified 25 CT-IPE algorithms through a systematic literature review and conducted a manual content analysis of their modeling assumptions and development contexts. To compare them meaningfully, we introduce a conceptual framework that distinguishes how algorithms generate, capture, and aggregate textual variance. On this basis, we identify four methodological families -- word-frequency, topic modeling, word embedding, and LLM-based approaches -- and critically assess their assumptions, interpretability, scalability, and limitations. Our review offers three contributions. First, it provides a structured synthesis of two decades of algorithm development, clarifying how diverse methods relate to one another. Second, it translates these insights into practical guidance for applied researchers, highlighting trade-offs in transparency, technical requirements, and validation strategies that shape algorithm choice. Third, it emphasizes that differences in estimation outcomes across algorithms are themselves informative, underscoring the need for systematic benchmarking.

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds, most existing approaches require access to specific input features, and rely on posterior mean and variance estimates or the tuning of hyperparameters. These limitations hinder robustness and fail to capture the model's global behavior in expectation. To address these limitations, we propose a chaining-based framework for estimating upper and lower bounds on the expected extreme values over unseen data, without requiring access to specific input features. We provide kernel-specific refinements for commonly used kernels such as RBF and Matérn, in which our bounds are tighter than generic constructions. We further improve numerical tightness by avoiding analytical relaxations. In addition to global estimation, we also develop a novel method for local uncertainty quantification at specified inputs. This approach leverages chaining geometry through partition diameters, adapting to local structures without relying on posterior variance scaling. Our experimental results validate the theoretical findings and demonstrate that our method outperforms existing approaches on both synthetic and real-world datasets.

The LogSumExp function, also known as the free energy, plays a central role in many important optimization problems, including entropy-regularized optimal transport and distributionally robust optimization (DRO). It is also the dual to the Kullback-Leibler (KL) divergence, which is widely used in machine learning. In practice, when the number of exponential terms inside the logarithm is large or infinite, optimization becomes challenging since computing the gradient requires differentiating every term. Previous approaches that replace the full sum with a small batch introduce significant bias. We propose a novel approximation to LogSumExp that can be efficiently optimized using stochastic gradient methods. This approximation is rooted in a sound modification of the KL divergence in the dual, resulting in a new $f$-divergence called the safe KL divergence. The accuracy of the approximation is controlled by a tunable parameter and can be made arbitrarily small. Like the LogSumExp, our approximation preserves convexity. Moreover, when applied to an $L$-smooth function bounded from below, the smoothness constant of the resulting objective scales linearly with $L$. Experiments in DRO and continuous optimal transport demonstrate the advantages of our approach over state-of-the-art baselines and the effective treatment of numerical issues associated with the standard LogSumExp and KL.

Chain-of-thought has been proven essential for enhancing the complex reasoning abilities of Large Language Models (LLMs), but it also leads to high computational costs. Recent advances have explored the method to route queries among multiple models and proved it as a promising approach. However, previous works directly operate at the task level, i.e., assigning user queries to suitable LLMs, which does not allow hybrid LLMs to truly collaborate on finer-grained sub-tasks. Collaboration at the level of intermediate reasoning steps (thoughts) could enable more efficient coordination, but it also poses significant challenges for router scheduling, placing immense demands on the quality of task decomposition and the precision of the router. To address this, we propose R2-Reasoner, a novel framework centered around a Reinforced Model Router designed to efficiently scale LLM reasoning. This router orchestrates collaboration across nine heterogeneous models, whose parameter scales range from less than 1B to hundreds of billions, by first breaking down a complex query into subtasks with a decomposer, and then assigning each subtask to the optimal model with a subtask allocator, balancing performance with cost. Training this router involves a two-stage alternating process for the decomposer and the allocator, integrating supervised fine-tuning with reinforcement learning to enable effective self-supervised refinement. Extensive experiments across six challenging reasoning benchmarks demonstrate that R2-Reasoner reduces API costs by 84.46% compared with state-of-the-art baselines while maintaining competitive reasoning accuracy. Our framework paves the way for the development of more scalable and efficient reasoning systems. Our code is open-source at https://anonymous.4open.science/r/R2_Reasoner.

Infinite hidden Markov models provide a flexible framework for modelling time series with structural changes and complex dynamics, without requiring the number of latent states to be specified in advance. This flexibility is achieved through the hierarchical Dirichlet process prior, while efficient Bayesian inference is enabled by the beam sampler, which combines dynamic programming with slice sampling to truncate the infinite state space adaptively. Despite extensive methodological developments, the role of initialization in this framework has received limited attention. This study addresses this gap by systematically evaluating initialization strategies commonly used for finite hidden Markov models and assessing their suitability in the infinite setting. Results from both simulated and real datasets show that distance-based clustering initializations consistently outperform model-based and uniform alternatives, the latter being the most widely adopted in the existing literature.

Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological signal processing highlight the importance of variables defined on topological spaces in several application domains. In such cases, the underlying topology shapes statistical relationships, limiting the expressiveness of canonical PGMs. To overcome this limitation, we introduce Colored Markov Random Fields (CMRFs), which model both conditional and marginal dependencies among Gaussian edge variables on topological spaces, with a theoretical foundation in Hodge theory. CMRFs extend classical Gaussian Markov Random Fields by including link coloring: connectivity encodes conditional independence, while color encodes marginal independence. We quantify the benefits of CMRFs through a distributed estimation case study over a physical network, comparing it with baselines with different levels of topological prior.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.