Related papers: Manifold Learning Using Kernel Density Estimation …

We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is…

Recently, building on the foundation of neural radiance field, various techniques have emerged to learn unsigned distance fields (UDF) to reconstruct 3D non-watertight models from multi-view images. Yet, a central challenge in UDF-based…

Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…

We study the quantitative convergence of Wasserstein gradient flows of Kernel Mean Discrepancy (KMD) (also known as Maximum Mean Discrepancy (MMD)) functionals. Our setting covers in particular the training dynamics of shallow neural…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

This work focuses on mitigating two limitations in the joint learning of local feature detectors and descriptors. First, the ability to estimate the local shape (scale, orientation, etc.) of feature points is often neglected during dense…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

Remote sensing image interpretation plays a critical role in environmental monitoring, urban planning, and disaster assessment. However, acquiring high-quality labeled data is often costly and time-consuming. To address this challenge, we…

Despite the great performance of deep learning models in many areas, they still make mistakes and underperform on certain subsets of data, i.e. error slices. Given a trained model, it is important to identify its semantically coherent error…

Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…

Meta-learning problem is usually formulated as a bi-level optimization in which the task-specific and the meta-parameters are updated in the inner and outer loops of optimization, respectively. However, performing the optimization in the…

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient…

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR…

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

Manifold structure learning is often used to exploit geometric information among data in semi-supervised feature learning algorithms. In this paper, we find that local discriminative information is also of importance for semi-supervised…

We present Masked Frequency Modeling (MFM), a unified frequency-domain-based approach for self-supervised pre-training of visual models. Instead of randomly inserting mask tokens to the input embeddings in the spatial domain, in this paper,…