Chain-of-Thought (CoT) technique has proven effective in improving the performance of large language models (LLMs) on complex reasoning tasks. However, the performance gains are inconsistent across different tasks, and the underlying mechanism remains a long-standing research question. In this work, we make a preliminary observation that the monotonicity of token probability distributions may be correlated with the gains achieved through CoT reasoning. Leveraging this insight, we propose two indicators based on the token probability distribution to assess CoT effectiveness across different tasks. By combining instance-level indicators with logistic regression model, we introduce Dynamic CoT, a method that dynamically select between CoT and direct answer. Furthermore, we extend Dynamic CoT to closed-source models by transferring decision strategies learned from open-source models. Our indicators for assessing CoT effectiveness achieve an accuracy of 89.2\%, and Dynamic CoT reduces token consumption by more than 35\% while maintaining high accuracy. Overall, our work offers a novel perspective on the underlying mechanisms of CoT reasoning and provides a framework for its more efficient deployment.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pre-training. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverages historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot settings with much better efficiency compared with existing time series foundation models.

Water reuse is a key point when fresh water is a commodity in ever greater demand, but which is also becoming ever more available. Furthermore, the return of clean water to its natural environment is also mandatory. Therefore, wastewater treatment plants (WWTPs) are essential in any policy focused on these serious challenges. WWTPs are complex facilities which need to operate at their best to achieve their goals. Nowadays, they are largely monitored, generating large databases of historical data concerning their functioning over time. All this implies a large amount of embedded information which is not usually easy for plant managers to assimilate, correlate and understand; in other words, for them to know the global operation of the plant at any given time. At this point, the intelligent and Machine Learning (ML) approaches can give support for that need, managing all the data and translating them into manageable, interpretable and explainable knowledge about how the WWTP plant is operating at a glance. Here, an eXplainable Artificial Intelligence (XAI) based methodology is proposed and tested for a real WWTP, in order to extract explainable service knowledge concerning the operation modes of the WWTP managed by AQUAVALL, which is the public service in charge of the integral water cycle in the City Council of Valladolid (Castilla y León, Spain). By applying well-known approaches of XAI and ML focused on the challenge of WWTP, it has been possible to summarize a large number of historical databases through a few explained operation modes of the plant in a low-dimensional data space, showing the variables and facility units involved in each case.

Accurate forecasting is key for all business planning. When estimated sales are too high, brick-and-mortar retailers may incur higher costs due to unsold inventories, higher labor and storage space costs, etc. On the other hand, when forecasts underestimate the level of sales, firms experience lost sales, shortages, and impact on the reputation of the retailer in their relevant market. Accurate forecasting presents a competitive advantage for companies. It facilitates the achievement of revenue and profit goals and execution of pricing strategy and tactics. In this study, we provide an exhaustive assessment of the forecasting models applied to a high-resolution brick-and-mortar retail dataset. Our forecasting framework addresses the problems found in retail environments, including intermittent demand, missing values, and frequent product turnover. We compare tree-based ensembles (such as XGBoost and LightGBM) and state-of-the-art neural network architectures (including N-BEATS, NHITS, and the Temporal Fusion Transformer) across various experimental settings. Our results show that localized modeling strategies especially those using tree-based models on individual groups with non-imputed data, consistently deliver superior forecasting accuracy and computational efficiency. In contrast, neural models benefit from advanced imputation methods, yet still fall short in handling the irregularities typical of physical retail data. These results further practical understanding for model selection in retail environment and highlight the significance of data preprocessing to improve forecast performance.

Accurately estimating the impact of road maintenance schedules on traffic conditions is important because maintenance operations can substantially worsen congestion if not carefully planned. Reliable estimates allow planners to avoid excessive delays during periods of roadwork. Since the exact increase in congestion is difficult to predict analytically, traffic simulations are commonly used to assess the redistribution of the flow of traffic. However, when applied to long-term maintenance planning involving many overlapping projects and scheduling alternatives, these simulations must be run thousands of times, resulting in a significant computational burden. This paper investigates the use of machine learning-based surrogate models to predict network-wide congestion caused by simultaneous road renovations. We frame the problem as a supervised learning task, using one-hot encodings, engineered traffic features, and heuristic approximations. A range of linear, ensemble-based, probabilistic, and neural regression models is evaluated under an online learning framework in which data progressively becomes available. The experimental results show that the Costliest Subset Heuristic provides a reasonable approximation when limited training data is available, and that most regression models fail to outperform it, with the exception of XGBoost, which achieves substantially better accuracy. In overall performance, XGBoost significantly outperforms alternatives in a range of metrics, most strikingly Mean Absolute Percentage Error (MAPE) and Pinball loss, where it achieves a MAPE of 11% and outperforms the next-best model by 20% and 38% respectively. This modeling approach has the potential to reduce the computational burden of large-scale traffic assignment problems in maintenance planning.

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating such games while capturing heterogeneity among players. In this paper, we propose and analyze a policy optimization framework for continuous-time, finite-horizon linear-quadratic GMFGs. Exploiting the structural properties of GMFGs, we design an efficient policy parameterization in which each player's policy is represented as an affine function of their private state, with a shared slope function and player-specific intercepts. We develop a bilevel optimization algorithm that alternates between policy gradient updates for best-response computation under a fixed population distribution, and distribution updates using the resulting policies. We prove linear convergence of the policy gradient steps to best-response policies and establish global convergence of the overall algorithm to the Nash equilibrium. The analysis relies on novel landscape characterizations over infinite-dimensional policy spaces. Numerical experiments demonstrate the convergence and robustness of the proposed algorithm under varying graphon structures, noise levels, and action frequencies.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

--Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in high-stakes applications. In domains such as medical diagnosis and financial risk assessment, algorithms must not only be accurate but also interpretable to ensure transparent and trustworthy decision-making. Therefore, to fill the gap of lack of interpretable algorithms in the field of clustering ensemble, we propose the first interpretable clustering ensemble algorithm in the literature. By treating base partitions as categorical variables, our method constructs a decision tree in the original feature space and use the statistical association test to guide the tree building process. Experimental results demonstrate that our algorithm achieves comparable performance to state-of-the-art (SOT A) clustering ensemble methods while maintaining an additional feature of interpretability. T o the best of our knowledge, this is the first interpretable algorithm specifically designed for clustering ensemble, offering a new perspective for future research in interpretable clustering. LUSTERING analysis [1] is an unsupervised learning issue in the field of data mining, which aims to partition data into different clusters by exploring its intrinsic structure.

Forecasting non-stationary time series is a challenging task because their statistical properties often change over time, making it hard for deep models to generalize well. Instance-level normalization techniques can help address shifts in temporal distribution. However, most existing methods overlook the multi-component nature of time series, where different components exhibit distinct non-stationary behaviors. In this paper, we propose Wavelet-based Disentangled Adaptive Normalization (WDAN), a model-agnostic framework designed to address non-stationarity in time series forecasting. WDAN uses discrete wavelet transforms to break down the input into low-frequency trends and high-frequency fluctuations. It then applies tailored normalization strategies to each part. For trend components that exhibit strong non-stationarity, we apply first-order differencing to extract stable features used for predicting normalization parameters. Extensive experiments on multiple benchmarks demonstrate that WDAN consistently improves forecasting accuracy across various backbone model. Code is available at this repository: https://github.com/MonBG/WDAN.

Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially problematic in applications like program fuzzing, where one wants to generate diverse and valid program inputs for testing purposes. We propose a new constrained sampling framework based on Markov Chain Monte Carlo (MCMC) that simultaneously satisfies three core desiderata: constraint satisfying (every sample satisfies the constraint), monotonically converging (the sampling process converges to the true conditional distribution), and efficient (high-quality samples emerge in few steps). Our method constructs a proposal distribution over valid outputs and applies a Metropolis-Hastings acceptance criterion based on the LM's likelihood, ensuring principled and efficient exploration of the constrained space. Empirically, our sampler outperforms existing methods on both synthetic benchmarks and real-world program fuzzing tasks.