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We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and…

Numerical Analysis · Mathematics 2025-06-11 Renjie Xu , Chong Wu , Maolin Che , Zhuoheng Ran , Yimin Wei , Hong Yan

We identify an issue in multi-task learnable compression, in which a representation learned for one task does not positively contribute to the rate-distortion performance of a different task as much as expected, given the estimated amount…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Anderson de Andrade , Ivan Bajić

We propose a method to learn object representations from 3D point clouds using bundles of geometrically interpretable hidden units, which we call geometric capsules. Each geometric capsule represents a visual entity, such as an object or a…

Machine Learning · Computer Science 2019-12-10 Nitish Srivastava , Hanlin Goh , Ruslan Salakhutdinov

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…

Computer Vision and Pattern Recognition · Computer Science 2024-10-10 Khalil Mathieu Hannouch , Stephan Chalup

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

Machine Learning · Computer Science 2026-04-14 Hanlin Yu , Søren Hauberg , Marcelo Hartmann , Arto Klami , Georgios Arvanitidis

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…

Machine Learning · Statistics 2016-10-06 Anthony L. Caterini , Dong Eui Chang

Projecting high-dimensional environment observations into lower-dimensional structured representations can considerably improve data-efficiency for reinforcement learning in domains with limited data such as robotics. Can a single generally…

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

Algebraic Topology · Mathematics 2024-06-26 Cheyne Glass , Elizabeth Vidaurre

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Optimization and Control · Mathematics 2026-02-17 Patrick L. Combettes , Javier I. Madariaga

Deep generative models have emerged as a powerful tool for learning useful molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. However, most existing deep…

Nowadays, supervised learning is commonly used in many domains. Indeed, many works propose to learn new knowledge from examples that translate the expected behaviour of the considered system. A key issue of supervised learning concerns the…

Machine Learning · Computer Science 2012-04-20 Patrick Taillandier , Alexis Drogoul

Text-to-CAD code generation is a long-horizon task that translates textual instructions into long sequences of interdependent operations. Existing methods typically decode text directly into executable code (e.g., bpy) without explicitly…

Artificial Intelligence · Computer Science 2026-04-14 Shengjie Gong , Wenjie Peng , Hongyuan Chen , Gangyu Zhang , Yunqing Hu , Huiyuan Zhang , Shuangping Huang , Tianshui Chen

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Computer Vision and Pattern Recognition · Computer Science 2019-02-20 Ankita Shukla , Shagun Uppal , Sarthak Bhagat , Saket Anand , Pavan Turaga

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Computational Engineering, Finance, and Science · Computer Science 2024-05-14 Gabriel Garayalde , Matteo Torzoni , Matteo Bruggi , Alberto Corigliano

We propose a method for self-supervised image representation learning under the guidance of 3D geometric consistency. Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply…

Computer Vision and Pattern Recognition · Computer Science 2022-03-30 Nenglun Chen , Lei Chu , Hao Pan , Yan Lu , Wenping Wang

We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…

Computational Geometry · Computer Science 2014-10-14 Paul Bendich , Ellen Gasparovic , John Harer , Rauf Izmailov , Linda Ness

With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to…

Machine Learning · Computer Science 2019-10-09 Antonia Gogoglou , C. Bayan Bruss , Keegan E. Hines

Coverage of image features play an important role in many vision algorithms since their distribution affect the estimated homography. This paper presents a Genetic Algorithm (GA) in order to select the optimal set of features yielding…

Computer Vision and Pattern Recognition · Computer Science 2017-04-21 Erkan Bostanci

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

Signal Processing · Electrical Eng. & Systems 2018-06-27 Ali Zare , Alp Ozdemir , Mark A. Iwen , Selin Aviyente

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically…

Machine Learning · Computer Science 2023-02-08 Giovanni Luca Marchetti , Gustaf Tegnér , Anastasiia Varava , Danica Kragic