Graph anomaly detection (GAD) is widely prevalent in scenarios such as financial fraud detection, anti-money laundering and social bot detecion. However, structural distribution shifts are commonly observed in real-world GAD data due to selection bias, resulting in reduced homophily. Existing GAD methods tend to rely on homophilic shortcuts when trained on high-homophily structures, limiting their ability to generalize well to data with low homophily under structural distribution shifts. In this study, we propose to handle structural distribution shifts by generating novel environments characterized by diverse homophilic structures and utilizing invariant patterns, i.e., features and structures with the capability of stable prediction across structural distribution shifts, which face two challenges: (1) How to discover invariant patterns from entangled features and structures, as structures are sensitive to varying homophilic distributions.

The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we design a new form of random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

Clustering is a fundamental problem that has been extensively studied over past few decades, with most research focusing on point-based clustering such as kmeans, k-median, and k-center. However, numerous real-world applications, such as motion analysis, computer vision, and missing data analysis, require clustering over structured data, including lines, time series and affine subspaces (flats), where traditional point-based clustering algorithms often fall short. In this paper, we study the k-means of lines problem, where the input is a set L of lines in Rd, and the goal is to find k centers C in Rd such that the sum of squared distances from each line in L to its nearest center in C is minimized. The local search algorithm is a well-established strategy for point-based k-means clustering, known for its efficiency and provable approximation guarantees. However, extending local search algorithm to the k-means of lines problem is nontrivial, as the capture relation used in point-based clustering does not generalize to the line setting.

Using pre-trained models has been found to reduce the effect of data heterogeneity and speed up federated learning algorithms. Recent works have explored trainingfree methods using first-and second-order statistics to aggregate local client data distributions at the server and achieve high performance without any training. In this work, we propose a training-free method based on an unbiased estimator of class covariance matrices which only uses first-order statistics in the form of class means communicated by clients to the server. We show how these estimated class covariances can be used to initialize the global classifier, thus exploiting the covariances without actually sharing them. We also show that using only withinclass covariances results in a better classifier initialization. Our approach improves performance in the range of 4-26% with exactly the same communication cost when compared to methods sharing only class means and achieves performance competitive or superior to methods sharing second-order statistics with dramatically less communication overhead. The proposed method is much more communicationefficient than federated prompt-tuning methods and still outperforms them. Finally, using our method to initialize classifiers and then performing federated fine-tuning or linear probing again yields better performance.

Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of functional data under fairness constraints, ensuring the disparity level of the classifier is controlled below a pre-specified threshold. We propose a unified framework for fairness-aware functional classification, tackling an infinite-dimensional functional space, addressing key challenges from the absence of density ratios and intractability of posterior probabilities, and discussing unique phenomena in functional classification. We further design a post-processing algorithm Fair Functional Linear Discriminant Analysis classifier (Fair-FLDA), which targets at homoscedastic Gaussian processes and achieves fairness via group-wise thresholding. Under weak structural assumptions on eigenspace, theoretical guarantees on fairness and excess risk controls are established. As a byproduct, our results cover the excess risk control of the standard FLDA as a special case, which, to the best of our knowledge, is first time seen. Our theoretical findings are complemented by extensive numerical experiments on synthetic and real datasets, highlighting the practicality of our designed algorithm.

We study the complexity of learning real-valued Multi-Index Models (MIMs) under the Gaussian distribution. AK-MIM is a function f: Rd R that depends only on the projection of its input onto a K-dimensional subspace. We give a general algorithm for PAC learning a broad class of MIMs with respect to the square loss, even in the presence of adversarial label noise. Moreover, we establish a nearly matching Statistical Query (SQ) lower bound, providing evidence that the complexity of our algorithm is qualitatively optimal as a function of the dimension. Specifically, we consider the class of bounded variation MIMs with the property that degree at most m distinguishing moments exist with respect to projections onto any subspace. In the presence of adversarial label noise, the complexity of our learning algorithm is dO(m)2poly(K/ϵ).

Achieving generalization in neural approaches across different scales and distributions remains a significant challenge for routing problems. A key obstacle is that neural networks often fail to learn robust principles for identifying universal patterns and deriving optimal solutions from diverse instances. In this paper, we first uncover Purity Law, a fundamental structural principle for optimal solutions of routing problems, defining that edge prevalence grows exponentially with the sparsity of surrounding vertices. Statistically and theoretically validated across diverse instances, Purity Law reveals a consistent bias toward local sparsity in global optima. Building on this insight, we propose Purity Policy Optimization (PUPO), a novel training paradigm that explicitly aligns characteristics of neural solutions with Purity Law during the solution construction process to enhance generalization. Extensive experiments demonstrate that PUPO can be seamlessly integrated with popular neural solvers, significantly enhancing their generalization performance without incurring additional computational overhead during inference. The code is available at https://github.com/Kejun0627/PUPO.

This work introduces a novel approach, Pairwise Epistemic Estimators (PairEpEsts), for epistemic uncertainty estimation in ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). By utilizing the pairwise distances between model components, PaiDEs establish bounds on entropy. We leverage this capability to enhance the performance of Bayesian Active Learning by Disagreement (BALD). Notably, unlike sample-based Monte Carlo estimators, PairEpEsts can estimate epistemic uncertainty up to 100 times faster and demonstrate superior performance in higher dimensions. To validate our approach, we conducted a varied series of regression experiments on commonly used benchmarks: 1D sinusoidal data, Pendulum, Hopper, Ant, and Humanoid, demonstrating PairEpEsts' advantage over baselines in high-dimensional regression active learning.

Data attribution for text-to-image models aims to identify the training images that most involv significantly e considerable influenced computational a generated resources output.

Test-Time Discovery (TTD) addresses the critical challenge of identifying and adapting to novel classes during inference while maintaining performance on known classes, which is a capability essential for dynamic real-world environments such as healthcare and autonomous driving. Recent TTD methods adopt training-free, memory-based strategies but rely on frozen models and static representations, resulting in poor generalization. In this paper, we propose a DiscrepancyAmplifying Adapter (DAA), a trainable module that enables real-time adaptation by amplifying feature-level discrepancies between known and unknown classes. During training, DAA is optimized using simulated unknowns and a novel warmup strategy to enhance its discriminative capacity. To ensure continual adaptation at test time, we introduce a Short-Term Memory Renewal (STMR) mechanism, which maintains a queue-based memory for unknown classes and selectively refreshes prototypes using recent, reliable samples. DAA is further updated through self-supervised learning, promoting knowledge retention for known classes while improving discrimination of emerging categories. Extensive experiments show that our method maintains high adaptability and stability, and significantly improves novel class discovery performance.