Time series classification involves learning a mapping from a continuous, temporally ordered sequence of real-valued observations to a discrete response variable, like class labels. This task is fundamental in domains, including health monitoring, where the temporal structure of data is critical for accurate prediction. Dynamic Time Warping (DTW) is a standard technique for measuring similarity between sequences varying in time or speed. However, DTW is restricted to discrete point matching. To move beyond pairwise alignment, we propose a theoretical framework that learns mappings between real-valued functions. These mappings approximate the flow associated with the characteristic curves of a linear transport equation with a space-dependent velocity field, providing a diffeomorphic transformation between two time series. Using the method of characteristics, we transform this partial differential equation into ordinary differential equations (ODEs) modeling system dynamics. The objective function used to learn these ODEs derives from the fundamental theorem of calculus. To enable flexible, expressive representations of the velocity field, we utilize reproducing kernel Hilbert spaces and optimal control methods. Our method, Diffeomorphic Time Warping (DiffTW), provides a theoretically grounded dissimilarity measure. Using a 1-nearest neighbor classifier, DiffTW outperforms DTW on 60 of 86 datasets.

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.

Data valuation quantifies the impact of individual data points on model performance, and Shapley values provide a principled approach to this important task due to their desirable axiomatic properties, albeit with high computational complexity. Recent breakthroughs have enabled fast computation of exact Shapley values for unweighted k-nearest neighbor (kNN) classifiers. However, extending this to weighted kNN models has remained a significant open challenge. The state-of-theart methods either require quadratic time complexity or resort to approximation via sampling. In this paper, we show that a conceptually simple but overlooked approach -- data duplication -- can be applied to this problem, yielding a natural variant of weighted kNN-Shapley. However, a straightforward application of the data-duplication idea leads to increased data size and prohibitive computational and memory costs. We develop an efficient algorithm that avoids materializing the duplicated dataset by exploiting the structural properties of weighted kNN models, reducing the complexity to near-linear time in the original data size. Besides, we establish theoretical foundations for this approach through axiomatic characterization of the resulting values, and empirically validate the effectiveness and efficiency of our method.

Data Shapley values provide a principled approach for quantifying the contribution of individual training examples to machine learning models. However, computing these values often requires computational complexity that is exponential in the data size, and this has led researchers to pursue efficient algorithms tailored to specific machine learning models. Building on the prior success of the Shapley valuation for K-nearest neighbor (KNN) models, in this paper, we introduce a localized data Shapley framework that significantly accelerates the valuation of data points.

Multi-view clustering aims to enhance clustering performance by leveraging information from diverse sources. However, its practical application is often hindered by a barrier: the lack of correspondences across views. This paper focuses on the understudied problem of fully incomplete multi-view clustering (FIMC), a scenario where existing methods fail due to their reliance on partial alignment. To address this problem, we introduce the Contrastive Prototype Matching Network (CPMN), a novel framework that establishes a new paradigm for cross-view alignment based on matching high-level categorical structures. Instead of aligning individual instances, CPMN performs a more robust cluster prototype alignment. CPMN first employs a correspondence-free graph contrastive learning approach, leveraging mutual k-nearest neighbors (MNN) to uncover intrinsic data structures and establish initial prototypes from entirely unpaired views. Building on the prototypes, we introduce a cross-view prototype graph matching stage to resolve category misalignment and forge a unified clustering structure. Finally, guided by this alignment, we devise a prototype-aware contrastive learning mechanism to promote semantic consistency, replacing the reliance on the initial MNN-based structural similarity. Extensive experiments on benchmark datasets demonstrate that our method significantly outperforms various baselines and ablation variants, validating its effectiveness.

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.

We introduce Autoregressive Retrieval Augmentation (AR-RAG), a novel paradigm that enhances image generation by autoregressively incorporating k-nearest neighbor retrievals at the patch level. Unlike prior methods that perform a single, static retrieval before generation and condition the entire generation on fixed reference images, AR-RAG performs context-aware retrievals at each generation step, using prior-generated patches as queries to retrieve and incorporate the most relevant patch-level visual references, enabling the model to respond to evolving generation needs while avoiding limitations (e.g., over-copying, stylistic bias, etc.) prevalent in existing methods. To realize AR-RAG, we propose two parallel frameworks: (1) Distribution-Augmentation in Decoding (DAiD), a training-free plug-and-use decoding strategy that directly merges the distribution of model-predicted patches with the distribution of retrieved patches, and (2) Feature-Augmentation in Decoding (FAiD), a parameter-efficient fine-tuning method that progressively smooths the features of retrieved patches via multi-scale convolution operations and leverages them to augment the image generation process. We validate the effectiveness of AR-RAG on widely adopted benchmarks, including Midjourney-30K, GenEval and DPG-Bench, demonstrating significant performance gains over state-of-the-art image generation models.

Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for datasets with more than a few dozen features. This paper introduces two complementary contributions that together reduce this cost by several orders of magnitude. The first contribution is an exact algebraic identity. This identity, derived from the orthogonality of the eigenvectors of the covariance matrix and the cyclicity of the trace operator, eliminates $H$ entirely and reduces the per-point cost to $O(m^2)$ after the eigendecomposition. The second contribution addresses the remaining $O(m^3)$ bottleneck of the full eigendecomposition. Since the local covariance matrix has rank at most $k-1 \ll m$, we replace it with a truncated SVD of the $k \times m$ centered data matrix, an $O(k^2 m)$ operation, and derive an analytical approximation for the contribution of the null-space eigenvectors based on the expected value of their outer product under the Haar measure. The resulting estimator has total cost $O(k^2 m + k m p^2)$, where $p = k-1$. Experiments on real-world datasets confirm speedups of 50 to 300 times relative to the original implementation, with negligible loss when the fast estimator is used to replace the original version. By providing a scalable and data-driven estimate of local curvature, the proposed method establishes curvature as a practical geometric feature for a broad range of machine learning tasks, from classical to modern deep learning pipelines.

Uniform sampling on implicitly defined manifolds is a core primitive in motion planning, constrained simulation, and probabilistic machine learning. MASEM addresses this problem by entropy-maximizing resampling, but its resampling weights depend on a local k-nearest-neighbour density estimate whose errors can be amplified by aggressive resampling temperatures. We ask whether a polynomial-maximization moment estimator can replace the plug-in density rule without changing the surrounding MASEM architecture. The proposed PMM-MASEM module computes shell spacings from nested k-nearest-neighbour radii, estimates their standardized cumulants, and uses a gated PMM2/PMM3 estimator only when the spacing distribution departs from the flat Exp(1) regime; otherwise it falls back to the plug-in/MLE rule. This fallback is essential: on a flat homogeneous manifold the plug-in estimator is already the MLE, so PMM should not outperform it. A local Known-DGP Monte Carlo experiment confirms this gate: the selector returns MLE on flat Exp(1) spacings and reduces density MSE by 22--36% on asymmetric gamma and boundary-spacing regimes. The evidence is not uniformly positive: PMM3 worsens a platykurtic uniform spacing law, and a lightweight resampling-proxy experiment improves seven-lobes coverage but degrades the sine and swiss-roll proxies. The current evidence therefore supports an applicability-boundary result rather than a general MASEM improvement claim.

The different cases represent various material property configurations. In Figure 8 we show the temporal evolution of different scenarios (a) to (d) for the initially straight bending rod, and (e) to (f) for the elastic helix. The default parameters of the initially straight bending rod are 0 =0, N = 30, ` =4 .0 In (b), we modify N 2{ 10,20,40,60}. The default parameters of the elastic helix are HR =0 .5 m (helix radius), HH =0 .5 m (helix height), HW =2 .5 (winding number), T =1 .0