--This paper presents a comprehensive comparative analysis of prominent clustering algorithms--K-means, DB-SCAN, and Spectral Clustering--on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering performance across multiple dimensionality reduction techniques (PCA, t-SNE, and UMAP) using diverse quantitative metrics. Experiments conducted on MNIST, Fashion-MNIST, and UCI HAR datasets reveal that preprocessing with UMAP consistently improves clustering quality across all algorithms, with Spectral Clustering demonstrating superior performance on complex manifold structures. Our findings show that algorithm selection should be guided by data characteristics, with K-means excelling in computational efficiency, DBSCAN in handling irregular clusters, and Spectral Clustering in capturing complex relationships. This research contributes a systematic approach for evaluating and selecting clustering techniques for high-dimensional data applications.

Link prediction also has significant implications from a fundamental point of view, as it allows for the identification of the elementary mechanisms behind the creation and decay of links in time-evolving networks (Leskovec et al., 2008). For example, triadic closure, at the core of standard methods of link prediction is considered as one of the driving forces for the creation of links in social networks (Kossinets and Watts, 2006). In general, link prediction consists in inferring the existence of a set of links from the observed structure of a network. The edges predicted may correspond to links that are bound to appear in the future, as in the seminal formulation by Liben-Nowell and Kleinberg (2007). They may also be existing links that have not been detected during the data collection process, in which case it is sometimes referred to as the missing link problem. In both cases, it can be described as a binary classification issue, where it is decided if a pair of nodes is connected or not. The features used are often based on the structural properties of the network of known interactions, either at a local scale (e.g. the number of common neighbors) or at a global scale (e.g.

Federated Learning is a popular paradigm that enables remote clients to jointly train a global model without sharing their raw data. However, FL has been shown to be vulnerable towards model poisoning attacks due to its distributed nature. Particularly, attackers acting as participants can upload arbitrary model updates that effectively compromise the global model of FL. While extensive research has been focusing on fighting against these attacks, we find that most of them assume data at remote clients are under iid while in practice they are inevitably non-iid. Our benchmark evaluations reveal that existing defenses generally fail to live up to their reputation when applied to various non-iid scenarios. In this paper, we propose a novel approach, GeminiGuard, that aims to address such a significant gap. We design GeminiGuard to be lightweight, versatile, and unsupervised so that it aligns well with the practical requirements of deploying such defenses. The key challenge from non-iids is that they make benign model updates look more similar to malicious ones. GeminiGuard is mainly built on two fundamental observations: (1) existing defenses based on either model-weight analysis or latent-space analysis face limitations in covering different MPAs and non-iid scenarios, and (2) model-weight and latent-space analysis are sufficiently different yet potentially complementary methods as MPA defenses. We hence incorporate a novel model-weight analysis component as well as a custom latent-space analysis component in GeminiGuard, aiming to further enhance its defense performance. We conduct extensive experiments to evaluate our defense across various settings, demonstrating its effectiveness in countering multiple types of untargeted and targeted MPAs, including adaptive ones. Our comprehensive evaluations show that GeminiGuard consistently outperforms SOTA defenses under various settings.

Sparse Mixture of Experts (SMoE) improves the efficiency of large language model training by directing input tokens to a subset of experts. Despite its success in generation tasks, its generalization ability remains an open question. In this paper, we demonstrate that current SMoEs, which fall into two categories: (1) Token Choice ;and (2) Expert Choice, struggle with tasks such as the Massive Text Embedding Benchmark (MTEB). By analyzing their mechanism through the lens of competitive learning, our study finds that the Token Choice approach may overly focus on irrelevant experts, while the Expert Choice approach risks discarding important tokens, potentially affecting performance. Motivated by this analysis, we propose Unified Competitive Learning SMoE (USMoE), a novel and efficient framework designed to improve the performance of existing SMoEs in both scenarios: with and without training. Extensive experiments across various tasks show that USMoE achieves up to a 10% improvement over traditional approaches or reduces computational inference costs by 14% while maintaining strong performance.

This paper proposes a unified theoretical framework based on the Kolmogorov-Arnold representation theorem and kernel methods. By analyzing the mathematical relationship among kernels, B-spline basis functions in Kolmogorov-Arnold Networks (KANs) and the inner product operation in self-attention mechanisms, we establish a kernel-based feature fitting framework that unifies the two models as linear combinations of kernel functions. Under this framework, we propose a low-rank Pseudo-Multi-Head Self-Attention module (Pseudo-MHSA), which reduces the parameter count of traditional MHSA by nearly 50\%. Furthermore, we design a Gaussian kernel multi-head self-attention variant (Gaussian-MHSA) to validate the effectiveness of nonlinear kernel functions in feature extraction. Experiments on the CIFAR-10 dataset demonstrate that Pseudo-MHSA model achieves performance comparable to the ViT model of the same dimensionality under the MAE framework and visualization analysis reveals their similarity of multi-head distribution patterns. Our code is publicly available.

The $k$-nearest-neighbor language model ($k$NN-LM), one of the retrieval-augmented language models, improves the perplexity for given text by directly accessing a large datastore built from any text data during inference. A widely held hypothesis for the success of $k$NN-LM is that its explicit memory, i.e., the datastore, enhances predictions for long-tail phenomena. However, prior works have primarily shown its ability to retrieve long-tail contexts, leaving the model's performance remain underexplored in estimating the probabilities of long-tail target tokens during inference. In this paper, we investigate the behavior of $k$NN-LM on low-frequency tokens, examining prediction probability, retrieval accuracy, token distribution in the datastore, and approximation error of the product quantization. Our experimental results reveal that $k$NN-LM does not improve prediction performance for low-frequency tokens but mainly benefits high-frequency tokens regardless of long-tail contexts in the datastore.

With the advance of high-throughput genotyping and sequencing technologies, it becomes feasible to comprehensive evaluate the role of massive genetic predictors in disease prediction. There exists, therefore, a critical need for developing appropriate statistical measurements to access the combined effects of these genetic variants in disease prediction. Predictiveness curve is commonly used as a graphical tool to measure the predictive ability of a risk prediction model on a single continuous biomarker. Yet, for most complex diseases, risk prediciton models are formed on multiple genetic variants. We therefore propose a multi-marker predictiveness curve and provide a non-parametric method to construct the curve for case-control studies. We further introduce a global predictiveness U and a partial predictiveness U to summarize prediction curve across the whole population and sub-population of clinical interest, respectively. We also demonstrate the connections of predictiveness curve with ROC curve and Lorenz curve. Through simulation, we compared the performance of the predictiveness U to other three summary indices: R square, Total Gain, and Average Entropy, and showed that Predictiveness U outperformed the other three indexes in terms of unbiasedness and robustness. Moreover, we simulated a series of rare-variants disease model, found partial predictiveness U performed better than global predictiveness U. Finally, we conducted a real data analysis, using predictiveness curve and predictiveness U to evaluate a risk prediction model for Nicotine Dependence.

This study proposes a novel framework for long-term electricity demand prediction based solely on historical consumption data, without relying on external variables such as temperature or economic indicators. The method combines Non-negative Tensor Factorization (NTF) to extract low-dimensional temporal features from multi-way electricity usage data, with a Genetic Algorithm that optimizes the hyperparameters of time series models applied to the latent annual factors. We model the dataset as a third-order tensor spanning electric utilities, industrial sectors, and years, and apply canonical polyadic decomposition under non-negativity constraints. The annual component is forecasted using autoregressive models, with hyperparameter tuning guided by the prediction error or reconstruction accuracy on a validation set. Comparative experiments using real-world electricity data from Japan demonstrate that the proposed method achieves lower mean squared error than baseline approaches without tensor decomposition or evolutionary optimization. Moreover, we find that reducing the model's degrees of freedom via tensor decomposition improves generalization performance, and that initialization sensitivity in NTF can be mitigated through multiple runs or ensemble strategies. These findings suggest that the proposed framework offers an interpretable, flexible, and scalable approach to long-term electricity demand prediction and can be extended to other structured time series forecasting tasks.

Long-term groundwater level (GWL) measurement is vital for effective policymaking and recharge estimation using annual maxima and minima. However, current methods prioritize short-term predictions and lack multi-year applicability, limiting their utility. Moreover, sparse in-situ measurements lead to reliance on low-resolution satellite data like GLDAS as the ground truth for Machine Learning models, further constraining accuracy. To overcome these challenges, we first develop an ML model to mitigate data gaps, achieving $R^2$ scores of 0.855 and 0.963 for maximum and minimum GWL predictions, respectively. Subsequently, using these predictions and well observations as ground truth, we train an Upsampling Model that uses low-resolution (25 km) GLDAS data as input to produce high-resolution (2 km) GWLs, achieving an excellent $R^2$ score of 0.96. Our approach successfully upscales GLDAS data for 2003-2024, allowing high-resolution recharge estimations and revealing critical trends for proactive resource management. Our method allows upsampling of groundwater storage (GWS) from GLDAS to high-resolution GWLs for any points independently of officially curated piezometer data, making it a valuable tool for decision-making.

The increasing integration of Artificial Intelligence across multiple industry sectors necessitates robust mechanisms for ensuring transparency, trust, and auditability of its development and deployment. This topic is particularly important in light of recent calls in various jurisdictions to introduce regulation and legislation on AI safety. In this paper, we propose a framework for complete verifiable AI pipelines, identifying key components and analyzing existing cryptographic approaches that contribute to verifiability across different stages of the AI lifecycle, from data sourcing to training, inference, and unlearning. This framework could be used to combat misinformation by providing cryptographic proofs alongside AI-generated assets to allow downstream verification of their provenance and correctness. Our findings underscore the importance of ongoing research to develop cryptographic tools that are not only efficient for isolated AI processes, but that are efficiently `linkable' across different processes within the AI pipeline, to support the development of end-to-end verifiable AI technologies.