Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image retrieval, recommendation systems, and cognitive psychology. The goal is to learn a metric in the RKHS that reflects the comparisons. Nonlinear metric learning using kernel methods and neural networks have shown great empirical promise. While previous works have addressed certain aspects of this problem, there is little or no theoretical understanding of such methods. The exception is the special (linear) case in which the RKHS is the standard Euclidean space $\mathbb{R}^d$; there is a comprehensive theory for metric learning in $\mathbb{R}^d$. This paper develops a general RKHS framework for metric learning and provides novel generalization guarantees and sample complexity bounds. We validate our findings through a set of simulations and experiments on real datasets. Our code is publicly available at https://github.com/RamyaLab/metric-learning-RKHS.

Confounders are extraneous variables that affect both the input and the target, resulting in spurious correlations and biased predictions. There are recent advances in dealing with or removing confounders in traditional models, such as metadata normalization (MDN), where the distribution of the learned features is adjusted based on the study confounders. However, in the context of continual learning, where a model learns continuously from new data over time without forgetting, learning feature representations that are invariant to confounders remains a significant challenge. To remove their influence from intermediate feature representations, we introduce the Recursive MDN (R-MDN) layer, which can be integrated into any deep learning architecture, including vision transformers, and at any model stage. R-MDN performs statistical regression via the recursive least squares algorithm to maintain and continually update an internal model state with respect to changing distributions of data and confounding variables. Our experiments demonstrate that R-MDN promotes equitable predictions across population groups, both within static learning and across different stages of continual learning, by reducing catastrophic forgetting caused by confounder effects changing over time.

Neural Radiance Field (NeRF)-based segmentation methods focus on object semantics and rely solely on RGB data, lacking intrinsic material properties. This limitation restricts accurate material perception, which is crucial for robotics, augmented reality, simulation, and other applications. W e introduce UnMix-NeRF, a framework that integrates spectral unmixing into NeRF, enabling joint hy-perspectral novel view synthesis and unsupervised material segmentation. Our method models spectral reflectance via diffuse and specular components, where a learned dictionary of global endmembers represents pure material signatures, and per-point abundances capture their distribution. F or material segmentation, we use spectral signature predictions along learned endmembers, allowing unsupervised material clustering. Additionally, UnMix-NeRF enables scene editing by modifying learned endmember dictionaries for flexible material-based appearance manipulation.

The segmentation of forest LiDAR 3D point clouds, including both individual tree and semantic segmentation, is fundamental for advancing forest management and ecological research. However, current approaches often struggle with the complexity and variability of natural forest environments. We present ForestFormer3D, a new unified and end-to-end framework designed for precise individual tree and semantic segmentation. ForestFormer3D incorporates ISA-guided query point selection, a score-based block merging strategy during inference, and a one-to-many association mechanism for effective training. By combining these new components, our model achieves state-of-the-art performance for individual tree segmentation on the newly introduced FOR-instanceV2 dataset, which spans diverse forest types and regions. Additionally, ForestFormer3D generalizes well to unseen test sets (Wytham woods and LAUTx), showcasing its robustness across different forest conditions and sensor modalities. The FOR-instanceV2 dataset and the ForestFormer3D code are publicly available at https://bxiang233.github.io/FF3D/.

Due to its nature of dynamic, mobility, and wireless data transfer, the Internet of Vehicles (IoV) is prone to various cyber threats, ranging from spoofing and Distributed Denial of Services (DDoS) attacks to malware. To safeguard the IoV ecosystem from intrusions, malicious activities, policy violations, intrusion detection systems (IDS) play a critical role by continuously monitoring and analyzing network traffic to identify and mitigate potential threats in real-time. However, most existing research has focused on developing centralized, machine learning-based IDS systems for IoV without accounting for its inherently distributed nature. Due to intensive computing requirements, these centralized systems often rely on the cloud to detect cyber threats, increasing delay of system response. On the other hand, edge nodes typically lack the necessary resources to train and deploy complex machine learning algorithms. To address this issue, this paper proposes an effective hierarchical classification framework tailored for IoV networks. Hierarchical classification allows classifiers to be trained and tested at different levels, enabling edge nodes to detect specific types of attacks independently. With this approach, edge nodes can conduct targeted attack detection while leveraging cloud nodes for comprehensive threat analysis and support. Given the resource constraints of edge nodes, we have employed the Boruta feature selection method to reduce data dimensionality, optimizing processing efficiency. To evaluate our proposed framework, we utilize the latest IoV security dataset CIC-IoV2024, achieving promising results that demonstrate the feasibility and effectiveness of our models in securing IoV networks.

We propose a generative, end-to-end solver for black-box combinatorial optimization that emphasizes both sample efficiency and solution quality on NP problems. Drawing inspiration from annealing-based algorithms, we treat the black-box objective as an energy function and train a neural network to model the associated Boltzmann distribution. By conditioning on temperature, the network captures a continuum of distributions--from near-uniform at high temperatures to sharply peaked around global optima at low temperatures--thereby learning the structure of the energy landscape and facilitating global optimization. When queries are expensive, the temperature-dependent distributions naturally enable data augmentation and improve sample efficiency. When queries are cheap but the problem remains hard, the model learns implicit variable interactions, effectively "opening" the black box. We validate our approach on challenging combinatorial tasks under both limited and unlimited query budgets, showing competitive performance against state-of-the-art black-box optimizers.

--Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. T o address these issues, we propose a deep spectral clustering model (named BootSC), which jointly learns all stages of spectral clustering-- affinity matrix construction, spectral embedding, and k -means clustering--using a single network in an end-to-end manner . Moreover, a semantically-consistent orthogonal re-parameterization technique is introduced to or-thogonalize spectral embeddings, significantly enhancing the discrimination capability. Experimental results indicate that BootSC achieves state-of-the-art clustering performance. For example, it accomplishes a notable 16% NMI improvement over the runner-up method on the challenging ImageNet-Dogs dataset. EEP clustering models aim to detect underlying cluster structures within unlabelled data. To train these models, creating effective and efficient supervision signals is necessary. Inadequate supervision could result in excessive computational costs [1], training instability [2], and degenerate results [3]. Classical deep clustering models [5], [6], [7], [8], [9], [10] commonly adopt cluster assignments obtained by k -means on data representations as training supervision. A major challenge with this k -means-style supervision is that data representations are assumed to follow simple isotropic Gaussian distributions.

The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and high computational cost. To address these issues, we propose a novel method, Stochastic Alternating Minimization with Trainable Step Sizes (SAMT), which updates network parameters in an alternating manner by treating the weights of each layer as a block. By decomposing the overall optimization into sub-problems corresponding to different blocks, this block-wise alternating strategy reduces per-step computational overhead and enhances training stability in nonconvex settings. To fully leverage these benefits, inspired by meta-learning, we proposed a novel adaptive step size strategy to incorporate into the sub-problem solving steps of alternating updates. It supports different types of trainable step sizes, including but not limited to scalar, element-wise, row-wise, and column-wise, enabling adaptive step size selection tailored to each block via meta-learning. We further provide a theoretical convergence guarantee for the proposed algorithm, establishing its optimization soundness. Extensive experiments for multiple benchmarks demonstrate that SAMT achieves better generalization performance with fewer parameter updates compared to state-of-the-art methods, highlighting its effectiveness and potential in neural network optimization.

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected neural networks, graph neural networks, clustering, and many-to-many comparisons of biological sequencing data. In many application scenarios, the matrix multiplication takes places on an arbitrary algebraic semiring where the scalar operations are overloaded with user-defined functions with certain properties or a more general heterogenous algebra where even the domains of the input matrices can be different. Here, we provide a unifying treatment of the sparse matrix-matrix operation and its rich application space including machine learning, computational biology and chemistry, graph algorithms, and scientific computing.

--Cluster analysis is a fundamental problem in data mining and machine learning. In recent years, multi-view clustering has attracted increasing attention due to its ability to integrate complementary information from multiple views. However, existing methods primarily focus on clustering performance, while fairness--a critical concern in human-centered applications--has been largely overlooked. Although recent studies have explored group fairness in multi-view clustering, most methods impose explicit regularization on cluster assignments, relying on the alignment between sensitive attributes and the underlying cluster structure. However, this assumption often fails in practice and can degrade clustering performance. In this paper, we propose an adversarial fair multi-view clustering (AFMVC) framework that integrates fairness learning into the representation learning process. Specifically, our method employs adversarial training to fundamentally remove sensitive attribute information from learned features, ensuring that the resulting cluster assignments are unaffected by it. Furthermore, we theoretically prove that aligning view-specific clustering assignments with a fairness-invariant consensus distribution via KL divergence preserves clustering consistency without significantly compromising fairness, thereby providing additional theoretical guarantees for our framework. Extensive experiments on data sets with fairness constraints demonstrate that AFMVC achieves superior fairness and competitive clustering performance compared to existing multi-view clustering and fairness-aware clustering methods. UL TI-view data [1] has been extensively utilized in a wide range of real-world applications in the era of big data, as the diverse information it captures is vital for effective data mining and analysis.