Prototypical Networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class.

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space.

We analyze the Kozachenko-Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent minimax lower bound over the H\{o}lder ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H\{o}lder ball for $s \in (0,2]$ and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

We analyze the Kozachenko-Leonenko (KL) fixed k -nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H older balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent mini-max lower bound over the H older ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H older ball for s (0, 2] and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in

The computational complexity of a property tester is the number of adjacency list entries it reads, denoted its queries . Many works in graph property testing focus on testing plain graphs that contain only the pure combinatorial information.

We propose a nonparametric estimator of multivariate joint entropy based on partitioned sample spacings (PSS). The method extends univariate spacing ideas to multivariate settings by partitioning the sample space into localized cells and aggregating within-cell statistics, with strong consistency guarantees under mild conditions. In benchmarks across diverse distributions, PSS consistently outperforms k-nearest neighbor estimators and achieves accuracy competitive with recent normalizing flow-based methods, while requiring no training or auxiliary density modeling. The estimator scales favorably in moderately high dimensions (d = 10 to 40) and shows particular robustness to correlated or skewed distributions. These properties position PSS as a practical alternative to normalizing flow-based approaches, with broad potential in information-theoretic machine learning applications.

The prevalence of real-world multi-view data makes incomplete multi-view clustering (IMVC) a crucial research. The rapid development of Graph Neural Networks (GNNs) has established them as one of the mainstream approaches for multi-view clustering. Despite significant progress in GNNs-based IMVC, some challenges remain: (1) Most methods rely on the K-Nearest Neighbors (KNN) algorithm to construct static graphs from raw data, which introduces noise and diminishes the robustness of the graph topology. (2) Existing methods typically utilize the Mean Squared Error (MSE) loss between the reconstructed graph and the sparse adjacency graph directly as the graph reconstruction loss, leading to substantial gradient noise during optimization. To address these issues, we propose a novel \textbf{D}ynamic Deep \textbf{G}raph Learning for \textbf{I}ncomplete \textbf{M}ulti-\textbf{V}iew \textbf{C}lustering with \textbf{M}asked Graph Reconstruction Loss (DGIMVCM). Firstly, we construct a missing-robust global graph from the raw data. A graph convolutional embedding layer is then designed to extract primary features and refined dynamic view-specific graph structures, leveraging the global graph for imputation of missing views. This process is complemented by graph structure contrastive learning, which identifies consistency among view-specific graph structures. Secondly, a graph self-attention encoder is introduced to extract high-level representations based on the imputed primary features and view-specific graphs, and is optimized with a masked graph reconstruction loss to mitigate gradient noise during optimization. Finally, a clustering module is constructed and optimized through a pseudo-label self-supervised training mechanism. Extensive experiments on multiple datasets validate the effectiveness and superiority of DGIMVCM.

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature's label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to drift noisy samples back to label-consistent representations. During adaptation, we sample from each target feature's latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier's accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve.

Unknown anomaly detection in medical imaging remains a fundamental challenge due to the scarcity of labeled anomalies and the high cost of expert supervision. We introduce an unsupervised, oracle-free framework that incrementally expands a trusted set of normal samples without any anomaly labels. Starting from a small, verified seed of normal images, our method alternates between lightweight adapter updates and uncertainty-gated sample admission. A frozen pretrained vision backbone is augmented with tiny convolutional adapters, ensuring rapid domain adaptation with negligible computational overhead. Extracted embeddings are stored in a compact coreset enabling efficient k-nearest neighbor anomaly (k-NN) scoring. Safety during incremental expansion is enforced by dual probabilistic gates, a sample is admitted into the normal memory only if its distance to the existing coreset lies within a calibrated z-score threshold, and its SWAG-based epistemic uncertainty remains below a seed-calibrated bound. This mechanism prevents drift and false inclusions without relying on generative reconstruction or replay buffers. Empirically, our system steadily refines the notion of normality as unlabeled data arrive, producing substantial gains over baselines. On COVID-CXR, ROC-AUC improves from 0.9489 to 0.9982 (F1: 0.8048 to 0.9746); on Pneumonia CXR, ROC-AUC rises from 0.6834 to 0.8968; and on Brain MRI ND-5, ROC-AUC increases from 0.6041 to 0.7269 and PR-AUC from 0.7539 to 0.8211. These results highlight the effectiveness and efficiency of the proposed framework for real-world, label-scarce medical imaging applications.