We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing approaches typically rely on smoothing techniques and are thus hindered by the curse of dimensionality. We propose a generalized notion of kernel-based conditional mean dependence that provides a new characterization of the null hypothesis of equal regression functions. Building on this reformulation, we develop two novel tests that leverage modern machine learning methods for flexible estimation. We establish the asymptotic properties of the test statistics, which hold under both fixed- and high-dimensional regimes. Unlike existing methods that often require restrictive distributional assumptions, our framework only imposes mild moment conditions. The efficacy of the proposed tests is demonstrated through extensive numerical studies.

Recent work has emphasized the diversification benefits of combining trend signals across multiple horizons, with the medium-term window-typically six months to one year-long viewed as the "sweet spot" of trend-following. This paper revisits this conventional view by reallocating exposure dynamically across horizons using a Bayesian optimization framework designed to learn the optimal weights assigned to each trend horizon at the asset level. The common practice of equal weighting implicitly assumes that all assets benefit equally from all horizons; we show that this assumption is both theoretically and empirically suboptimal. We first optimize the horizon-level weights at the asset level to maximize the informativeness of trend signals before applying Bayesian graphical models-with sparsity and turnover control-to allocate dynamically across assets. The key finding is that the medium-term band contributes little incremental performance or diversification once short- and long-term components are included. Removing the 125-day layer improves Sharpe ratios and drawdown efficiency while maintaining benchmark correlation. We then rationalize this outcome through a minimum-variance formulation, showing that the medium-term horizon largely overlaps with its neighboring horizons. The resulting "barbell" structure-combining short- and long-term trends-captures most of the performance while reducing model complexity. This result challenges the common belief that more horizons always improve diversification and suggests that some forms of time-scale diversification may conceal unnecessary redundancy in trend premia.

Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget.

Accurate prediction of ionic conductivity in electrolyte systems is crucial for advancing numerous scientific and technological applications. While significant progress has been made, current research faces two fundamental challenges: (1) the lack of high-quality standardized benchmarks, and (2) inadequate modeling of geometric structure and intermolecular interactions in mixture systems. To address these limitations, we first reorganize and enhance the CALiSol and DiffMix electrolyte datasets by incorporating geometric graph representations of molecules. We then propose GeoMix, a novel geometry-aware framework that preserves Set-SE(3) equivariance-an essential but challenging property for mixture systems. At the heart of GeoMix lies the Geometric Interaction Network (GIN), an equivariant module specifically designed for intermolecular geometric message passing. Comprehensive experiments demonstrate that GeoMix consistently outperforms diverse baselines (including MLPs, GNNs, and geometric GNNs) across both datasets, validating the importance of cross-molecular geometric interactions and equivariant message passing for accurate property prediction. This work not only establishes new benchmarks for electrolyte research but also provides a general geometric learning framework that advances modeling of mixture systems in energy materials, pharmaceutical development, and beyond.

User interests on content platforms are inherently diverse, manifesting through complex behavioral patterns across heterogeneous scenarios such as search, feed browsing, and content discovery. Traditional recommendation systems typically prioritize business metric optimization within isolated specific scenarios, neglecting cross-scenario behavioral signals and struggling to integrate advanced techniques like LLMs at billion-scale deployments, which finally limits their ability to capture holistic user interests across platform touchpoints. We propose RED-Rec, an LLM-enhanced hierarchical Recommender Engine for Diversified scenarios, tailored for industry-level content recommendation systems. RED-Rec unifies user interest representations across multiple behavioral contexts by aggregating and synthesizing actions from varied scenarios, resulting in comprehensive item and user modeling. At its core, a two-tower LLM-powered framework enables nuanced, multifaceted representations with deployment efficiency, and a scenario-aware dense mixing and querying policy effectively fuses diverse behavioral signals to capture cross-scenario user intent patterns and express fine-grained, context-specific intents during serving. We validate RED-Rec through online A/B testing on hundreds of millions of users in RedNote through online A/B testing, showing substantial performance gains in both content recommendation and advertisement targeting tasks. We further introduce a million-scale sequential recommendation dataset, RED-MMU, for comprehensive offline training and evaluation. Our work advances unified user modeling, unlocking deeper personalization and fostering more meaningful user engagement in large-scale UGC platforms.

Deep neural networks (DNNs) play a significant role in an increasing body of research on traffic forecasting due to their effectively capturing spatiotemporal patterns embedded in traffic data. A general assumption of training the said forecasting models via mean squared error estimation is that the errors across time steps and spatial positions are uncorrelated. However, this assumption does not really hold because of the autocorrelation caused by both the temporality and spatiality of traffic data. This gap limits the performance of DNN-based forecasting models and is overlooked by current studies. To fill up this gap, this paper proposes Spatiotemporally Autocorrelated Error Adjustment (SAEA), a novel and general framework designed to systematically adjust autocorrelated prediction errors in traffic forecasting. Unlike existing approaches that assume prediction errors follow a random Gaussian noise distribution, SAEA models these errors as a spatiotemporal vector autoregressive (VAR) process to capture their intrinsic dependencies. First, it explicitly captures both spatial and temporal error correlations by a coefficient matrix, which is then embedded into a newly formulated cost function. Second, a structurally sparse regularization is introduced to incorporate prior spatial information, ensuring that the learned coefficient matrix aligns with the inherent road network structure. Finally, an inference process with test-time error adjustment is designed to dynamically refine predictions, mitigating the impact of autocorrelated errors in real-time forecasting. The effectiveness of the proposed approach is verified on different traffic datasets. Results across a wide range of traffic forecasting models show that our method enhances performance in almost all cases.

While Generative AI rapidly advances in various domains, generating truly creative, aesthetic, and counter-intuitive outputs remains a challenge. This paper presents an approach to tackle these difficulties in the domain of chess puzzles. We start by benchmarking Generative AI architectures, and then introduce an RL framework with novel rewards based on chess engine search statistics to overcome some of those shortcomings. The rewards are designed to enhance a puzzle's uniqueness, counter-intuitiveness, diversity, and realism. Our RL approach dramatically increases counter-intuitive puzzle generation by 10x, from 0.22\% (supervised) to 2.5\%, surpassing existing dataset rates (2.1\%) and the best Lichess-trained model (0.4\%). Our puzzles meet novelty and diversity benchmarks, retain aesthetic themes, and are rated by human experts as more creative, enjoyable, and counter-intuitive than composed book puzzles, even approaching classic compositions. Our final outcome is a curated booklet of these AI-generated puzzles, which is acknowledged for creativity by three world-renowned experts.

Unmanned aerial vehicles (UAVs) are emerging as key enablers for low-altitude wireless network (LAWN), particularly when terrestrial networks are unavailable. In such scenarios, the environmental topology is typically unknown; hence, designing efficient and safe UAV trajectories is essential yet challenging. To address this, we propose a digital twin (DT)-assisted training and deployment framework. In this framework, the UAV transmits integrated sensing and communication signals to provide communication services to ground users, while simultaneously collecting echoes that are uploaded to the DT server to progressively construct virtual environments (VEs). These VEs accelerate model training and are continuously updated with real-time UAV sensing data during deployment, supporting decision-making and enhancing flight safety. Based on this framework, we further develop a trajectory design scheme that integrates simulated annealing for efficient user scheduling with the twin-delayed deep deterministic policy gradient algorithm for continuous trajectory design, aiming to minimize mission completion time while ensuring obstacle avoidance. Simulation results demonstrate that the proposed approach achieves faster convergence, higher flight safety, and shorter mission completion time compared with baseline methods, providing a robust and efficient solution for LAWN deployment in unknown environments.

Understanding and forecasting precipitation events in the Arctic maritime environments, such as Bear Island and Ny-Ålesund, is crucial for assessing climate risk and developing early warning systems in vulnerable marine regions. This study proposes a probabilistic machine learning framework for modeling and predicting the dynamics and severity of precipitation. We begin by analyzing the scale-dependent relationships between precipitation and key atmospheric drivers (e.g., temperature, relative humidity, cloud cover, and air pressure) using wavelet coherence, which captures localized dependencies across time and frequency domains. To assess joint causal influences, we employ Synergistic-Unique-Redundant Decomposition, which quantifies the impact of interaction effects among each variable on future precipitation dynamics. These insights inform the development of data-driven forecasting models that incorporate both historical precipitation and causal climate drivers. To account for uncertainty, we employ the conformal prediction method, which enables the generation of calibrated non-parametric prediction intervals. Our results underscore the importance of utilizing a comprehensive framework that combines causal analysis with probabilistic forecasting to enhance the reliability and interpretability of precipitation predictions in Arctic marine environments.

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.