pwc-archive/papers-with-abstracts huggingface dataset:
Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference
Authors: Frank Shih, Zhenghao Jiang, Faming Liang
Date: 2025-05-25 00:00:00
Tasks: Uncertainty Quantification

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.
Do Large Language Models (Really) Need Statistical Foundations?
Authors: Weijie Su
Date: 2025-05-25 00:00:00
Tasks: Uncertainty Quantification

Large language models (LLMs) represent a new paradigm for processing unstructured data, with applications across an unprecedented range of domains. In this paper, we address, through two arguments, whether the development and application of LLMs would genuinely benefit from foundational contributions from the statistics discipline. First, we argue affirmatively, beginning with the observation that LLMs are inherently statistical models due to their profound data dependency and stochastic generation processes, where statistical insights are naturally essential for handling variability and uncertainty. Second, we argue that the persistent black-box nature of LLMs -- stemming from their immense scale, architectural complexity, and development practices often prioritizing empirical performance over theoretical interpretability -- renders closed-form or purely mechanistic analyses generally intractable, thereby necessitating statistical approaches due to their flexibility and often demonstrated effectiveness. To substantiate these arguments, the paper outlines several research areas -- including alignment, watermarking, uncertainty quantification, evaluation, and data mixture optimization -- where statistical methodologies are critically needed and are already beginning to make valuable contributions. We conclude with a discussion suggesting that statistical research concerning LLMs will likely form a diverse ``mosaic'' of specialized topics rather than deriving from a single unifying theory, and highlighting the importance of timely engagement by our statistics community in LLM research.
BroadGen: A Framework for Generating Effective and Efficient Advertiser Broad Match Keyphrase Recommendations
Authors: Ashirbad Mishra, Jinyu Zhao, Soumik Dey, Hansi Wu, Binbin Li, Kamesh Madduri
Date: 2025-05-25 00:00:00
Tasks: Management

In the domain of sponsored search advertising, the focus of Keyphrase recommendation has largely been on exact match types, which pose issues such as high management expenses, limited targeting scope, and evolving search query patterns. Alternatives like Broad match types can alleviate certain drawbacks of exact matches but present challenges like poor targeting accuracy and minimal supervisory signals owing to limited advertiser usage. This research defines the criteria for an ideal broad match, emphasizing on both efficiency and effectiveness, ensuring that a significant portion of matched queries are relevant. We propose BroadGen, an innovative framework that recommends efficient and effective broad match keyphrases by utilizing historical search query data. Additionally, we demonstrate that BroadGen, through token correspondence modeling, maintains better query stability over time. BroadGen's capabilities allow it to serve daily, millions of sellers at eBay with over 2.3 billion items.
PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders
Authors: Michail Spitieris, Massimiliano Ruocco, Abdulmajid Murad, Alessandro Nocente
Date: 2025-05-25 00:00:00
Tasks: Diversity, Synthetic Data Generation

Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data by incorporating physical constraints to enhance performance. Specifically, we extend the VAE architecture by incorporating physical models in the generative process, enabling it to capture underlying dynamics more effectively. While physical models provide valuable insights, they struggle to capture complex temporal dependencies present in real-world data. To bridge this gap, we introduce a discrepancy term to account for unmodeled dynamics, represented within a latent Gaussian Process VAE (GPVAE). Furthermore, we apply regularization to ensure the generated data aligns closely with observed data, enhancing both the diversity and accuracy of the synthetic samples. The proposed method is applied to indoor temperature data, achieving state-of-the-art performance. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.
Adaptive Diffusion Guidance via Stochastic Optimal Control
Authors: Iskander Azangulov, Peter Potaptchik, Qinyu Li, Eddie Aamari, George Deligiannidis, Judith Rousseau
Date: 2025-05-25 00:00:00
Tasks: Scheduling

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate guidance weight--are largely heuristic and lack a solid theoretical foundation. This work addresses these limitations on two fronts. First, we provide a theoretical formalization that precisely characterizes the relationship between guidance strength and classifier confidence. Second, building on this insight, we introduce a stochastic optimal control framework that casts guidance scheduling as an adaptive optimization problem. In this formulation, guidance strength is not fixed but dynamically selected based on time, the current sample, and the conditioning class, either independently or in combination. By solving the resulting control problem, we establish a principled foundation for more effective guidance in diffusion models.
Foundations of Top-$k$ Decoding For Language Models
Authors: Georgy Noarov, Soham Mallick, Tao Wang, Sunay Joshi, Yan Sun, Yangxinyu Xie, Mengxin Yu, Edgar Dobriban
Date: 2025-05-25 00:00:00
Tasks: Unity

Top-$k$ decoding is a widely used method for sampling from LLMs: at each token, only the largest $k$ next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-$k$ and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-$k$ decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-$k$ decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We consider \emph{Bregman decoders} obtained by minimizing a separable Bregman divergence (for both the \emph{primal} and \emph{dual} cases) with a sparsity-inducing $\ell_0$ regularization. Despite the combinatorial nature of the objective, we show how to optimize it efficiently for a large class of divergences. We show that the optimal decoding strategies are greedy, and further that the loss function is discretely convex in $k$, so that binary search provably and efficiently finds the optimal $k$. We show that top-$k$ decoding arises as a special case for the KL divergence, and identify new decoding strategies that have distinct behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).
Uniform convergence of the smooth calibration error and its relationship with functional gradient
Authors: Futoshi Futami, Atsushi Nitanda
Date: 2025-05-26 00:00:00

Calibration is a critical requirement for reliable probabilistic prediction, especially in high-risk applications. However, the theoretical understanding of which learning algorithms can simultaneously achieve high accuracy and good calibration remains limited, and many existing studies provide empirical validation or a theoretical guarantee in restrictive settings. To address this issue, in this work, we focus on the smooth calibration error (CE) and provide a uniform convergence bound, showing that the smooth CE is bounded by the sum of the smooth CE over the training dataset and a generalization gap. We further prove that the functional gradient of the loss function can effectively control the training smooth CE. Based on this framework, we analyze three representative algorithms: gradient boosting trees, kernel boosting, and two-layer neural networks. For each, we derive conditions under which both classification and calibration performances are simultaneously guaranteed. Our results offer new theoretical insights and practical guidance for designing reliable probabilistic models with provable calibration guarantees.
Toward Physics-Informed Machine Learning for Data Center Operations: A Tropical Case Study
Authors: Ruihang Wang, Zhiwei Cao, Qingang Zhang, Rui Tan, Yonggang Wen, Tommy Leung, Stuart Kennedy, Justin Teoh
Date: 2025-05-26 00:00:00
Tasks: Physics-informed machine learning

Data centers are the backbone of computing capacity. Operating data centers in the tropical regions faces unique challenges due to consistently high ambient temperature and elevated relative humidity throughout the year. These conditions result in increased cooling costs to maintain the reliability of the computing systems. While existing machine learning-based approaches have demonstrated potential to elevate operations to a more proactive and intelligent level, their deployment remains dubious due to concerns about model extrapolation capabilities and associated system safety issues. To address these concerns, this article proposes incorporating the physical characteristics of data centers into traditional data-driven machine learning solutions. We begin by introducing the data center system, including the relevant multiphysics processes and the data-physics availability. Next, we outline the associated modeling and optimization problems and propose an integrated, physics-informed machine learning system to address them. Using the proposed system, we present relevant applications across varying levels of operational intelligence. A case study on an industry-grade tropical data center is provided to demonstrate the effectiveness of our approach. Finally, we discuss key challenges and highlight potential future directions.
Origin Tracer: A Method for Detecting LoRA Fine-Tuning Origins in LLMs
Authors: Hongyu Liang, Yuting Zheng, Yihan Li, Yiran Zhang, Shiyu Liang
Date: 2025-05-26 00:00:00

As large language models (LLMs) continue to advance, their deployment often involves fine-tuning to enhance performance on specific downstream tasks. However, this customization is sometimes accompanied by misleading claims about the origins, raising significant concerns about transparency and trust within the open-source community. Existing model verification techniques typically assess functional, representational, and weight similarities. However, these approaches often struggle against obfuscation techniques, such as permutations and scaling transformations. To address this limitation, we propose a novel detection method Origin-Tracer that rigorously determines whether a model has been fine-tuned from a specified base model. This method includes the ability to extract the LoRA rank utilized during the fine-tuning process, providing a more robust verification framework. This framework is the first to provide a formalized approach specifically aimed at pinpointing the sources of model fine-tuning. We empirically validated our method on thirty-one diverse open-source models under conditions that simulate real-world obfuscation scenarios. We empirically analyze the effectiveness of our framework and finally, discuss its limitations. The results demonstrate the effectiveness of our approach and indicate its potential to establish new benchmarks for model verification.
Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variables
Authors: Futoshi Futami, Masahiro Fujisawa
Date: 2025-05-26 00:00:00
Tasks: Data Compression, Decoder

Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in supervised learning, similar analyses for unsupervised models such as variational autoencoders (VAEs) remain insufficiently underexplored. In this work, we extend information-theoretic generalization analysis to vector-quantized (VQ) VAEs with discrete latent spaces, introducing a novel data-dependent prior to rigorously analyze the relationship among LVs, generalization, and data generation. We derive a novel generalization error bound of the reconstruction loss of VQ-VAEs, which depends solely on the complexity of LVs and the encoder, independent of the decoder. Additionally, we provide the upper bound of the 2-Wasserstein distance between the distributions of the true data and the generated data, explaining how the regularization of the LVs contributes to the data generation performance.
Unlocking the Power of Diffusion Models in Sequential Recommendation: A Simple and Effective Approach
Authors: Jialei Chen, Yuanbo Xu, Yiheng Jiang
Date: 2025-05-26 00:00:00
Tasks: Denoising, Recommendation Systems, Sequential Recommendation

In this paper, we focus on the often-overlooked issue of embedding collapse in existing diffusion-based sequential recommendation models and propose ADRec, an innovative framework designed to mitigate this problem. Diverging from previous diffusion-based methods, ADRec applies an independent noise process to each token and performs diffusion across the entire target sequence during training. ADRec captures token interdependency through auto-regression while modeling per-token distributions through token-level diffusion. This dual approach enables the model to effectively capture both sequence dynamics and item representations, overcoming the limitations of existing methods. To further mitigate embedding collapse, we propose a three-stage training strategy: (1) pre-training the embedding weights, (2) aligning these weights with the ADRec backbone, and (3) fine-tuning the model. During inference, ADRec applies the denoising process only to the last token, ensuring that the meaningful patterns in historical interactions are preserved. Our comprehensive empirical evaluation across six datasets underscores the effectiveness of ADRec in enhancing both the accuracy and efficiency of diffusion-based sequential recommendation systems.
MSD-LLM: Predicting Ship Detention in Port State Control Inspections with Large Language Model
Authors: Jiongchao Jin, Xiuju Fu, Xiaowei Gao, Tao Cheng, Ran Yan
Date: 2025-05-26 00:00:00
Tasks: Language Modeling, Language Modelling, Large Language Model, Representation Learning

Maritime transportation is the backbone of global trade, making ship inspection essential for ensuring maritime safety and environmental protection. Port State Control (PSC), conducted by national ports, enforces compliance with safety regulations, with ship detention being the most severe consequence, impacting both ship schedules and company reputations. Traditional machine learning methods for ship detention prediction are limited by the capacity of representation learning and thus suffer from low accuracy. Meanwhile, autoencoder-based deep learning approaches face challenges due to the severe data imbalance in learning historical PSC detention records. To address these limitations, we propose Maritime Ship Detention with Large Language Models (MSD-LLM), integrating a dual robust subspace recovery (DSR) layer-based autoencoder with a progressive learning pipeline to handle imbalanced data and extract meaningful PSC representations. Then, a large language model groups and ranks features to identify likely detention cases, enabling dynamic thresholding for flexible detention predictions. Extensive evaluations on 31,707 PSC inspection records from the Asia-Pacific region show that MSD-LLM outperforms state-of-the-art methods more than 12\% on Area Under the Curve (AUC) for Singapore ports. Additionally, it demonstrates robustness to real-world challenges, making it adaptable to diverse maritime risk assessment scenarios.
A Structured Tour of Optimization with Finite Differences
Authors: Marco Rando, Cesare Molinari, Lorenzo Rosasco, Silvia Villa
Date: 2025-05-26 00:00:00

Finite-difference methods are widely used for zeroth-order optimization in settings where gradient information is unavailable or expensive to compute. These procedures mimic first-order strategies by approximating gradients through function evaluations along a set of random directions. From a theoretical perspective, recent studies indicate that imposing structure (such as orthogonality) on the chosen directions allows for the derivation of convergence rates comparable to those achieved with unstructured random directions (i.e., directions sampled independently from a distribution). Empirically, although structured directions are expected to enhance performance, they often introduce additional computational costs, which can limit their applicability in high-dimensional settings. In this work, we examine the impact of structured direction selection in finite-difference methods. We review and extend several strategies for constructing structured direction matrices and compare them with unstructured approaches in terms of computational cost, gradient approximation quality, and convergence behavior. Our evaluation spans both synthetic tasks and real-world applications such as adversarial perturbation. The results demonstrate that structured directions can be generated with computational costs comparable to unstructured ones while significantly improving gradient estimation accuracy and optimization performance.
Accelerating Nash Learning from Human Feedback via Mirror Prox
Authors: Daniil Tiapkin, Daniele Calandriello, Denis Belomestny, Eric Moulines, Alexey Naumov, Kashif Rasul, Michal Valko, Pierre Menard
Date: 2025-05-26 00:00:00

Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley-Terry model, which may not accurately capture the complexities of real human preferences (e.g., intransitivity). Nash Learning from Human Feedback (NLHF) offers a more direct alternative by framing the problem as finding a Nash equilibrium of a game defined by these preferences. In this work, we introduce Nash Mirror Prox ($\mathtt{Nash-MP}$), an online NLHF algorithm that leverages the Mirror Prox optimization scheme to achieve fast and stable convergence to the Nash equilibrium. Our theoretical analysis establishes that Nash-MP exhibits last-iterate linear convergence towards the $\beta$-regularized Nash equilibrium. Specifically, we prove that the KL-divergence to the optimal policy decreases at a rate of order $(1+2\beta)^{-N/2}$, where $N$ is a number of preference queries. We further demonstrate last-iterate linear convergence for the exploitability gap and uniformly for the span semi-norm of log-probabilities, with all these rates being independent of the size of the action space. Furthermore, we propose and analyze an approximate version of Nash-MP where proximal steps are estimated using stochastic policy gradients, making the algorithm closer to applications. Finally, we detail a practical implementation strategy for fine-tuning large language models and present experiments that demonstrate its competitive performance and compatibility with existing methods.
Weighted Leave-One-Out Cross Validation
Authors: Luc Pronzato, Maria-João Rendas
Date: 2025-05-26 00:00:00
Tasks: Model Selection

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite collection of sites. The method relies on the construction of the best linear estimator of the squared prediction error at an arbitrary unsampled site based on squared LOO residuals, assuming that the function is a realization of a Gaussian Process (GP). A theoretical analysis of performance of the ISE estimator is presented, and robustness with respect to the choice of the GP kernel is investigated first analytically, then through numerical examples. Overall, the estimation of ISE is significantly more precise than with classical, unweighted, LOO cross validation. Application to model selection is briefly considered through examples.
Cellwise and Casewise Robust Covariance in High Dimensions
Authors: Fabio Centofanti, Mia Hubert, Peter J. Rousseeuw
Date: 2025-05-26 00:00:00
Tasks: Anomaly Detection

The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating cells (entries) of the data matrix. Recently some robust covariance estimators have been developed that can handle both types of outliers, but their computation is only feasible up to at most 20 dimensions. To remedy this we propose the cellRCov method, a robust covariance estimator that simultaneously handles casewise outliers, cellwise outliers, and missing data. It relies on a decomposition of the covariance on principal and orthogonal subspaces, leveraging recent work on robust PCA. It also employs a ridge-type regularization to stabilize the estimated covariance matrix. We establish some theoretical properties of cellRCov, including its casewise and cellwise influence functions as well as consistency and asymptotic normality. A simulation study demonstrates the superior performance of cellRCov in contaminated and missing data scenarios. Furthermore, its practical utility is illustrated in a real-world application to anomaly detection. We also construct and illustrate the cellRCCA method for robust and regularized canonical correlation analysis.