Related papers: The Manifold Scattering Transform for High-Dimensi…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

The irregular domain and lack of ordering make it challenging to design deep neural networks for point cloud processing. This paper presents a novel framework named Point Cloud Transformer(PCT) for point cloud learning. PCT is based on…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…

Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative…

Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new…

Recently, deep neural networks have made remarkable achievements in 3D point cloud classification. However, existing classification methods are mainly implemented on idealized point clouds and suffer heavy degradation of per-formance on…

Data imputation and data generation have important applications for many domains, like healthcare and finance, where incomplete or missing data can hinder accurate analysis and decision-making. Diffusion models have emerged as powerful…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored.…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…

Analyzing the geometric and semantic properties of 3D point clouds through the deep networks is still challenging due to the irregularity and sparsity of samplings of their geometric structures. This paper presents a new method to define…

Snapshot multi-dimensional imaging offers a promising alternative to traditional low-dimensional imaging techniques by enabling the simultaneous capture of spatial, spectral, polarization, and other information in a single shot for improved…

Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

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…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…