This paper introduces innovative enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces. Unlike traditional distance metrics, Gini-based measures incorporate both value-based and rank-based information, improving robustness to noise and outliers. The main contributions of this work include: proposing a Gini-based measure that captures both rank information and value distances; presenting a Gini K-means algorithm that is proven to converge and demonstrates resilience to noisy data; and introducing a Gini KNN method that performs competitively with state-of-the-art approaches such as Hassanat's distance in noisy environments. Experimental evaluations on 14 datasets from the UCI repository demonstrate the superior performance and efficiency of Gini-based algorithms in clustering and classification tasks. This work opens new avenues for leveraging rank-based measures in machine learning and statistical analysis.

The rapid emergence of single-cell data has facilitated the study of many different biological conditions at the cellular level. Cluster analysis has been widely applied to identify cell types, capturing the essential patterns of the original data in a much more concise form. One challenge in the cluster analysis of cells is matching clusters extracted from datasets of different origins or conditions. Many existing algorithms cannot recognize new cell types present in only one of the two samples when establishing a correspondence between clusters obtained from two samples. Additionally, when there are more than two samples, it is advantageous to align clusters across all samples simultaneously rather than performing pairwise alignment. Our approach aims to construct a taxonomy for cell clusters across all samples to better annotate these clusters and effectively extract features for downstream analysis. A new system for constructing cell-type taxonomy has been developed by combining the technique of Optimal Transport with Relaxed Marginal Constraints (OT-RMC) and the simultaneous alignment of clusters across multiple samples. OT-RMC allows us to address challenges that arise when the proportions of clusters vary substantially between samples or when some clusters do not appear in all the samples. Experiments on more than twenty datasets demonstrate that the taxonomy constructed by this new system can yield highly accurate annotation of cell types. Additionally, sample-level features extracted based on the taxonomy result in accurate classification of samples.

Existing actor-critic algorithms, which are popular for continuous control reinforcement learning (RL) tasks, suffer from poor sample efficiency due to lack of principled exploration mechanism within them. Motivated by the success of Thompson sampling for efficient exploration in RL, we propose a novel model-free RL algorithm, Langevin Soft Actor Critic (LSAC), which prioritizes enhancing critic learning through uncertainty estimation over policy optimization. LSAC employs three key innovations: approximate Thompson sampling through distributional Langevin Monte Carlo (LMC) based $Q$ updates, parallel tempering for exploring multiple modes of the posterior of the $Q$ function, and diffusion synthesized state-action samples regularized with $Q$ action gradients. Our extensive experiments demonstrate that LSAC outperforms or matches the performance of mainstream model-free RL algorithms for continuous control tasks. Notably, LSAC marks the first successful application of an LMC based Thompson sampling in continuous control tasks with continuous action spaces.

The constant engagement with extensive written materials is fundamental and immensely time-consuming [104]. Legal professionals often spend hours, if not days, combing through documents to find precedents or relevant cases that could be pivotal to their current cases. This laborious process is a significant part of the workload of legal professionals like lawyers and judges, taking up lots of time that could be invested otherwise. Automatic summarization tools could help to condense lengthy legal documents into concise summaries, helping to save both time and costs. Moreover, integrating advanced Natural Language Processing (NLP) techniques into legal research holds significant promise for democratizing access to legal information. Figure 1 shows the general pipeline for legal summarization. Compared to other domains, legal texts present unique challenges that distinguish them from other document types. Legal documents tend to be longer and more detailed than those from other domains.

Battery health monitoring is critical for the efficient and reliable operation of electric vehicles (EVs). This study introduces a transformer-based framework for estimating the State of Health (SoH) and predicting the Remaining Useful Life (RUL) of lithium titanate (LTO) battery cells by utilizing both cycle-based and instantaneous discharge data. Testing on eight LTO cells under various cycling conditions over 500 cycles, we demonstrate the impact of charge durations on energy storage trends and apply Differential Voltage Analysis (DVA) to monitor capacity changes (dQ/dV) across voltage ranges. Our LLM model achieves superior performance, with a Mean Absolute Error (MAE) as low as 0.87\% and varied latency metrics that support efficient processing, demonstrating its strong potential for real-time integration into EVs. The framework effectively identifies early signs of degradation through anomaly detection in high-resolution data, facilitating predictive maintenance to prevent sudden battery failures and enhance energy efficiency.

We study decentralized optimization over a network of agents, modeled as graphs, with no central server. The goal is to minimize $f+r$, where $f$ represents a (strongly) convex function averaging the local agents' losses, and $r$ is a convex, extended-value function. We introduce DCatalyst, a unified black-box framework that integrates Nesterov acceleration into decentralized optimization algorithms. %, enhancing their performance. At its core, DCatalyst operates as an \textit{inexact}, \textit{momentum-accelerated} proximal method (forming the outer loop) that seamlessly incorporates any selected decentralized algorithm (as the inner loop). We demonstrate that DCatalyst achieves optimal communication and computational complexity (up to log-factors) across various decentralized algorithms and problem instances. Notably, it extends acceleration capabilities to problem classes previously lacking accelerated solution methods, thereby broadening the effectiveness of decentralized methods. On the technical side, our framework introduce the {\it inexact estimating sequences}--a novel extension of the well-known Nesterov's estimating sequences, tailored for the minimization of composite losses in decentralized settings. This method adeptly handles consensus errors and inexact solutions of agents' subproblems, challenges not addressed by existing models.

The Isolation Forest (iForest), proposed by Liu, Ting, and Zhou at TKDE 2012, has become a prominent tool for unsupervised anomaly detection. However, recent research by Hariri, Kind, and Brunner, published in TKDE 2021, has revealed issues with iForest. They identified the presence of axis-aligned ghost clusters that can be misidentified as normal clusters, leading to biased anomaly scores and inaccurate predictions. In response, they developed the Extended Isolation Forest (EIF), which effectively solves these issues by eliminating the ghost clusters introduced by iForest. This enhancement results in improved consistency of anomaly scores and superior performance. We reveal a previously overlooked problem in the Extended Isolation Forest (EIF), showing that it is vulnerable to ghost inter-clusters between normal clusters of data points. In this paper, we introduce the Rotated Isolation Forest (RIF) algorithm which effectively addresses both the axis-aligned ghost clusters observed in iForest and the ghost inter-clusters seen in EIF. RIF accomplishes this by randomly rotating the dataset (using random rotation matrices and QR decomposition) before feeding it into the iForest construction, thereby increasing dataset variation and eliminating ghost clusters. Our experiments conclusively demonstrate that the RIF algorithm outperforms iForest and EIF, as evidenced by the results obtained from both synthetic datasets and real-world datasets.

When designing materials to optimize certain properties, there are often many possible configurations of designs that need to be explored. For example, the materials' composition of elements will affect properties such as strength or conductivity, which are necessary to know when developing new materials. Exploring all combinations of elements to find optimal materials becomes very time consuming, especially when there are more design variables. For this reason, there is growing interest in using machine learning (ML) to predict a material's properties. In this work, we model the optimization of certain material properties as a tensor completion problem, to leverage the structure of our datasets and navigate the vast number of combinations of material configurations. Across a variety of material property prediction tasks, our experiments show tensor completion methods achieving 10-20% decreased error compared with baseline ML models such as GradientBoosting and Multilayer Perceptron (MLP), while maintaining similar training speed.

Recent developments in Self-Supervised Learning (SSL) have demonstrated significant potential for Speaker Verification (SV), but closing the performance gap with supervised systems remains an ongoing challenge. Standard SSL frameworks rely on anchor-positive pairs extracted from the same audio utterances. Hence, positives have channel characteristics similar to those of their corresponding anchors, even with extensive data-augmentation. Therefore, this positive sampling strategy is a fundamental limitation as it encodes too much information regarding the recording source in the learned representations. This article introduces Self-Supervised Positive Sampling (SSPS), a bootstrapped technique for sampling appropriate and diverse positives in SSL frameworks for SV. SSPS samples positives close to their anchor in the representation space, as we assume that these pseudo-positives belong to the same speaker identity but correspond to different recording conditions. This method demonstrates consistent improvements in SV performance on VoxCeleb benchmarks when implemented in major SSL frameworks, such as SimCLR, SwAV, VICReg, and DINO. Using SSPS, SimCLR, and DINO achieve 2.57% and 2.53% EER on VoxCeleb1-O. SimCLR yields a 58% relative reduction in EER, getting comparable performance to DINO with a simpler training framework. Furthermore, SSPS lowers intra-class variance and reduces channel information in speaker representations while exhibiting greater robustness without data-augmentation.

As one of the most promising methods in self-supervised learning, contrastive learning has achieved a series of breakthroughs across numerous fields. A predominant approach to implementing contrastive learning is applying InfoNCE loss: By capturing the similarities between pairs, InfoNCE loss enables learning the representation of data. Albeit its success, adopting InfoNCE loss requires tuning a temperature, which is a core hyperparameter for calibrating similarity scores. Despite its significance and sensitivity to performance being emphasized by several studies, searching for a valid temperature requires extensive trial-and-error-based experiments, which increases the difficulty of adopting InfoNCE loss. To address this difficulty, we propose a novel method to deploy InfoNCE loss without temperature. Specifically, we replace temperature scaling with the inverse hyperbolic tangent function, resulting in a modified InfoNCE loss. In addition to hyperparameter-free deployment, we observed that the proposed method even yielded a performance gain in contrastive learning. Our detailed theoretical analysis discovers that the current practice of temperature scaling in InfoNCE loss causes serious problems in gradient descent, whereas our method provides desirable gradient properties. The proposed method was validated on five benchmarks on contrastive learning, yielding satisfactory results without temperature tuning.