Related papers: When Locally Linear Embedding Hits Boundary

The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…

Line detection is widely used in many robotic tasks such as scene recognition, 3D reconstruction, and simultaneous localization and mapping (SLAM). Compared to points, lines can provide both low-level and high-level geometrical information…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

Unsupervised attributed graph representation learning is challenging since both structural and feature information are required to be represented in the latent space. Existing methods concentrate on learning latent representation via…

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism…

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…

We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements.Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is…

Learning-based edge detection has hereunto been strongly supervised with pixel-wise annotations which are tedious to obtain manually. We study the problem of self-training edge detection, leveraging the untapped wealth of large-scale…

We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. We derive several new algorithms for dynamic programming and…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

Our goal is to understand how post-training methods, such as fine-tuning, alignment, and unlearning, modify language model behavior and representations. We are particularly interested in the brittle nature of these modifications that makes…

Dense prediction tasks typically employ encoder-decoder architectures, but the prevalent convolutions in the decoder are not image-adaptive and can lead to boundary artifacts. Different generalized convolution operations have been…

We analyze an approximation of a Laplacian subject to non-local interface conditions of a $\delta'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence…

While texture analysis is largely addressed for images, the comparison of the geometric reliefs on surfaces embedded in the 3D space is still an open challenge. Starting from the Local Binary Pattern (LBP) description originally defined for…

Samples from intimate (non-linear) mixtures are generally modeled as being drawn from a smooth manifold. Scenarios where the data contains multiple intimate mixtures with some constituent materials in common can be thought of as manifolds…

An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through…

However, real-world data often exhibit complex local structures that can be challenging for single-model approaches with a smooth global manifold in the embedding space to unravel. In this work, we conjecture that in the latent space of…