Related papers: An Incremental Non-Linear Manifold Approximation M…

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…

Effectively retrieving, reasoning, and understanding multimodal information remains a critical challenge for agentic systems. Traditional Retrieval-augmented Generation (RAG) methods rely on linear interaction histories, which struggle to…

Data augmentation is widely known as a simple yet surprisingly effective technique for regularizing deep networks. Conventional data augmentation schemes, e.g., flipping, translation or rotation, are low-level, data-independent and…

High-dimensional astronomical data cubes provide a wealth of spectral and structural information that can be used to study astrophysical and chemical processes. The complexity and sheer size of these datasets pose significant challenges in…

Solving quantifier-free non-linear real arithmetic (NRA) problems is a computationally hard task. To tackle this problem, prior work proposed a promising approach based on gradient descent. In this work, we extend their ideas and combine…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

In the field of 3D dynamic scene reconstruction, how to balance model convergence rate and rendering quality has long been a critical challenge that urgently needs to be addressed, particularly in high-precision modeling of scenes with…

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…

Unsupervised fault detection in multivariate time series plays a vital role in ensuring the stable operation of complex systems. Traditional methods often assume that normal data follow a single Gaussian distribution and identify anomalies…

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…

Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…

Guided depth super-resolution (GDSR) reconstructs HR depth maps from LR inputs with HR RGB guidance. Existing methods either model each modality independently or rely on computationally expensive attention mechanisms with quadratic…

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional…

We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…

Domain adaptation remains a challenge when there is significant manifold discrepancy between source and target domains. Although recent methods leverage manifold-aware adversarial perturbations to perform data augmentation, they often…

In this paper, we present an effective data augmentation framework leveraging the Large Language Model (LLM) and Diffusion Model (DM) to tackle the challenges inherent in data-scarce scenarios. Recently, DMs have opened up the possibility…