The random vector functional link (RVFL) neural network has shown significant potential in overcoming the constraints of traditional artificial neural networks, such as excessive computation time and suboptimal solutions. However, RVFL faces challenges when dealing with noise and outliers, as it assumes all data samples contribute equally. To address this issue, we propose a novel robust framework, R2VFL, RVFL with Huber weighting function and class probability, which enhances the model's robustness and adaptability by effectively mitigating the impact of noise and outliers in the training data. The Huber weighting function reduces the influence of outliers, while the class probability mechanism assigns less weight to noisy data points, resulting in a more resilient model. We explore two distinct approaches for calculating class centers within the R2VFL framework: the simple average of all data points in each class and the median of each feature, the later providing a robust alternative by minimizing the effect of extreme values. These approaches give rise to two novel variants of the model-R2VFL-A and R2VFL-M. We extensively evaluate the proposed models on 47 UCI datasets, encompassing both binary and multiclass datasets, and conduct rigorous statistical testing, which confirms the superiority of the proposed models. Notably, the models also demonstrate exceptional performance in classifying EEG signals, highlighting their practical applicability in real-world biomedical domain.

--Federated domain generalization (FedDG) aims to learn a globally generalizable model from decentralized clients with heterogeneous data while preserving privacy. Recent studies have introduced prompt learning to adapt vision-language models (VLMs) in FedDG by learning a single global prompt. However, such a one-prompt-fits-all learning paradigm typically leads to performance degradation on personalized samples. Although the mixture of experts (MoE) offers a promising solution for specialization, existing MoE-based methods suffer from coarse image-level expert assignment and high communication costs from parameterized routers. T o address these limitations, we propose TRIP, a T oken-level pRompt mIxture with Parameter-free routing framework for FedDG, which treats multiple prompts as distinct experts. Unlike existing image-level routing designs, TRIP assigns different tokens within an image to specific experts. T o ensure communication efficiency, TRIP incorporates a parameter-free routing mechanism based on token clustering and optimal transport. The instance-specific prompt is then synthesized by aggregating experts, weighted by the number of tokens assigned to each. Additionally, TRIP develops an unbiased learning strategy for prompt experts, leveraging the VLM's zero-shot generalization capability. Extensive experiments across four benchmarks demonstrate that TRIP achieves optimal generalization results, with communicating only 1K parameters per round. HE exponential growth of data from diverse and decentralized sources has significantly accelerated advancements in machine learning. However, traditional machine learning paradigms typically operate in a centralized manner, which requires all decentralized data to be processed on a central server, raising serious privacy concerns. This work was supported by the Shandong Provincial Natural Science Foundation under Grant ZR2020KF015, and by the Taishan Scholar Program of Shandong Province under Grant tsqn202211199 and Grant tstp20221137. S. Gong, C. Cui, and X. Dong are with the School of Computing and Artificial Intelligence, Shandong University of Finance and Economics, Jinan 250014, China (e-mail: gsh8210@163.com; X. Nie is with the School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250101, China (e-mail: niexsh@hotmail.com). L. Zhu is with the College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China (e-mail: leizhu0608@gmail.com). X. Chang is with the School of Information Science and Technology, University of Science and Technology of China, Anhui 230026, China.

With the growing presence of multilingual users on social media, detecting abusive language in code-mixed text has become increasingly challenging. Code-mixed communication, where users seamlessly switch between English and their native languages, poses difficulties for traditional abuse detection models, as offensive content may be context-dependent or obscured by linguistic blending. While abusive language detection has been extensively explored for high-resource languages like English and Hindi, low-resource languages such as Telugu and Nepali remain underrepresented, leaving gaps in effective moderation. In this study, we introduce a novel, manually annotated dataset of 2 thousand Telugu-English and 5 Nepali-English code-mixed comments, categorized as abusive and non-abusive, collected from various social media platforms. The dataset undergoes rigorous preprocessing before being evaluated across multiple Machine Learning (ML), Deep Learning (DL), and Large Language Models (LLMs). We experimented with models including Logistic Regression, Random Forest, Support Vector Machines (SVM), Neural Networks (NN), LSTM, CNN, and LLMs, optimizing their performance through hyperparameter tuning, and evaluate it using 10-fold cross-validation and statistical significance testing (t-test). Our findings provide key insights into the challenges of detecting abusive language in code-mixed settings and offer a comparative analysis of computational approaches. This study contributes to advancing NLP for low-resource languages by establishing benchmarks for abusive language detection in Telugu-English and Nepali-English code-mixed text. The dataset and insights can aid in the development of more robust moderation strategies for multilingual social media environments.

Due to the vast number of students enrolled in programming courses, there has been an increasing number of automated program repair techniques focused on introductory programming assignments (IPAs). Typically, such techniques use program clustering to take advantage of previous correct student implementations to repair a new incorrect submission. These repair techniques use clustering methods since analyzing all available correct submissions to repair a program is not feasible. However, conventional clustering methods rely on program representations based on features such as abstract syntax trees (ASTs), syntax, control flow, and data flow. This paper proposes InvAASTCluster, a novel approach for program clustering that uses dynamically generated program invariants to cluster semantically equivalent IPAs. InvAASTCluster's program representation uses a combination of the program's semantics, through its invariants, and its structure through its anonymized abstract syntax tree (AASTs). Invariants denote conditions that must remain true during program execution, while AASTs are ASTs devoid of variable and function names, retaining only their types. Our experiments show that the proposed program representation outperforms syntax-based representations when clustering a set of correct IPAs. Furthermore, we integrate InvAASTCluster into a state-of-the-art clustering-based program repair tool. Our results show that InvAASTCluster advances the current state-of-the-art when used by clustering-based repair tools by repairing around 13% more students' programs, in a shorter amount of time.

This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of Gaussian measures. This invariance serves as the foundation for constructing a reduced gradient structure on the parameter space characterizing Gaussian densities. We derive explicit ordinary differential equations that govern the evolution of mean, covariance, and mass under the HK-Boltzmann gradient flow. The reduced structure retains the additive form of the HK metric, facilitating a comprehensive analysis of the dynamics involved. We explore the geodesic convexity of the reduced system, revealing that global convexity is confined to the pure transport scenario, while a variant of sublevel semi-convexity is observed in the general case. Furthermore, we demonstrate exponential convergence to equilibrium through Polyak-Lojasiewicz-type inequalities, applicable both globally and on sublevel sets. By monitoring the evolution of covariance eigenvalues, we refine the decay rates associated with convergence. Additionally, we extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity, corroborating our theoretical results with numerical experiments that encompass a Gaussian-target gradient flow and a Bayesian logistic regression application.

In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the major challenges in modern day large-scale learning. A classical way to represent heterogeneous data is via a mixture model. In this paper, we study generalization performance and statistical rates when data is sampled from a mixture distribution. We first characterize the heterogeneity of the mixture in terms of the pairwise total variation distance of the sub-population distributions. Thereafter, as a central theme of this paper, we characterize the range where the mixture may be treated as a single (homogeneous) distribution for learning. In particular, we study the generalization performance under the classical PAC framework and the statistical error rates for parametric (linear regression, mixture of hyperplanes) as well as non-parametric (Lipschitz, convex and Hölder-smooth) regression problems. In order to do this, we obtain Rademacher complexity and (local) Gaussian complexity bounds with mixture data, and apply them to get the generalization and convergence rates respectively. We observe that as the (regression) function classes get more complex, the requirement on the pairwise total variation distance gets stringent, which matches our intuition. We also do a finer analysis for the case of mixed linear regression and provide a tight bound on the generalization error in terms of heterogeneity.

REGULAR ARTICLE Sparse mixed linear modeling with anchor-based guidance for high-entropy alloy discovery Ryo Murakami a, Seiji Miura b, Akihiro Endo a and Satoshi Minamoto a a Materials Data Platform, Research Network and Facility Services Division, National Institute for Materials Science, Tsukuba 305-0044, Ibaraki, Japan b Division of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Hokkaido, Japan ARTICLE HISTORY Compiled April 30, 2025 ABSTRACT High-entropy alloys have attracted attention for their exceptional mechanical properties and thermal stability. To solve this problem, machine learning techniques have been increasingly employed for property prediction and high-throughput screening. Nevertheless, highly accurate nonlinear models often suffer from a lack of interpretability, which is a major limitation. In this study, we focus on local data structures that emerge from the greedy search behavior inherent to experimental data acquisition. By introducing a linear and low-dimensional mixture regression model, we strike a balance between predictive performance and model interpretability. In addition, we develop an algorithm that simultaneously performs prediction and feature selection by considering multiple candidate descriptors. Through a case study on high-entropy alloys, this study introduces a method that combines anchor-guided clustering and sparse linear modeling to address biased data structures arising from greedy exploration in materials science. KEYWORDS Sparse modeling; Mixed linear model; Bayesian inference; Materials informatics; Data-driven science; High-entropy alloys 1. Introduction In recent years, high-entropy alloys (HEAs) have garnered attention as next-generation materials for their outstanding mechanical properties, thermal stability, and corrosion resistance [1,2]. Unlike conventional alloy designs, HEAs--also referred to as multi-principal element alloys--comprise multiple (typically five or more) principal elements, offering a high degree of chemical and structural freedom. This unique composition enables the exploration of novel properties unattainable in traditional materials systems.

Financial data analysis plays a pivotal role in today's business landscape [1, 2, 3, 4, 5, 6, 7], including credit risk assessment (such as loan prediction and credit scoring), fraud detection, and cost optimization, etc. However, when we develop solutions to address financial problems, we will inevitably encounter a number of key challenges [1, 2, 3, 4, 5]. For example, financial data is often voluminous, dynamically and frequently generated in real time, and distributed across diverse locations, making it challenging to process and analyze in a centralized manner[1], e.g., the New Y ork Stock Exchange (NYSE) alone has billions of transactions per day. Similarly, other major exchanges, such as the Shanghai Stock Exchange (SSE) and the London Stock Exchange (LSE), also generate vast amounts of stock data. Additionally, noise and missing values unavoidably occur in financial data, which can cause results and predictions to be skewed (or even completely wrong). These challenges require firms to come up with more efficient and smarter solutions. In recent decades, machine learning has achieved remarkable success across various domains [8, 9, 10], owing to its effective generalization ability and adaptability, and has also received increasing attention in financial data analysis [11, 12], such as credit risk assessment, resource allocation, and cost optimization. However, these classical (supervised) machine learning based solutions, such as logistic regression and random forest, usually implicitly assume that 1) all the data is stored and centralized at one location, typically a single machine, and that we have full access to the entire data; 2) these algorithms expect to run on a single machine with minimal concerns for memory or disk storage limitations; and 3) the provided data is clean and free from outliers introduced by malicious adversaries, as it is stored at a single location equipped with high security protection mechanisms to prevent data corruption. Nonetheless, these assumptions do not always hold in practice.

We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis space. These lower bounds imply that kernel interpolation is always inconsistent, when the smoothness index of the norm is larger than a constant that depends only on the embedding index of the hypothesis space and the decay rate of the eigenvalues.

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best approximates the input points. More precisely, for a given $p\geq 1$, we aim to minimize the $p$th power of the $\ell_p$ norm of the error vector $(\|a_1-\bm{P}a_1\|,\ldots,\|a_n-\bm{P}a_n\|)$, where $\bm{P}$ denotes the projection matrix onto the subspace and the norms are Euclidean. In \emph{constrained} subspace approximation (CSA), we additionally have constraints on the projection matrix $\bm{P}$. In its most general form, we require $\bm{P}$ to belong to a given subset $\mathcal{S}$ that is described explicitly or implicitly. We introduce a general framework for constrained subspace approximation. Our approach, that we term coreset-guess-solve, yields either $(1+\varepsilon)$-multiplicative or $\varepsilon$-additive approximations for a variety of constraints. We show that it provides new algorithms for partition-constrained subspace approximation with applications to {\it fair} subspace approximation, $k$-means clustering, and projected non-negative matrix factorization, among others. Specifically, while we reconstruct the best known bounds for $k$-means clustering in Euclidean spaces, we improve the known results for the remainder of the problems.