Related papers: Adaptive Geometric Regression for High-Dimensional…

Automated 3D scene generation is pivotal for applications spanning virtual reality, digital content creation, and Embodied AI. While computer graphics prioritizes aesthetic layouts, vision and robotics demand scenes that mirror real-world…

The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…

We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods have shown great potential through bypassing the detection of repeatable keypoints which is difficult to do especially in…

Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse…

Understanding how nano- or micro-scale structures and material properties can be optimally configured to attain specific functionalities remains a fundamental challenge. Photonic metasurfaces, for instance, can be spectrally tuned through…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

The proliferation of floating anthropogenic debris in rivers has emerged as a pressing environmental concern, exerting a detrimental influence on biodiversity, water quality, and human activities such as navigation and recreation. The…

In this work we provide an analysis of the distribution of the post-adaptation parameters of Gradient-Based Meta-Learning (GBML) methods. Previous work has noticed how, for the case of image-classification, this adaptation only takes place…

The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

The reconstruction of 3D microstructures from 2D slices is considered to hold significant value in predicting the spatial structure and physical properties of materials.The dimensional extension from 2D to 3D is viewed as a highly…

Super-resolving the coarse outputs of global climate simulations, termed downscaling, is crucial in making political and social decisions on systems requiring long-term climate change projections. Existing fast super-resolution techniques,…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…

We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…