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Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects…

Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…

Quasi parton distribution functions (QPDFs) are defined in terms of QCD fields at spacelike separations evaluated in matrix elements of hadrons moving with velocity $v$. These objects can be studied in lattice QCD. In the limit when $v$…

Deep learning-based super-resolution (SR) methods often perform pixel-wise computations uniformly across entire images, even in homogeneous regions where high-resolution refinement is redundant. We propose the Quadtree Diffusion Model…

Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on…

In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation of 6D pose, it cannot represent an uncertainty of the observation. In order to…

Multimodal medical imaging provides complementary information that is crucial for accurate delineation of pathology, but the development of deep learning models is limited by the scarcity of large datasets in which different modalities are…

Mapping the conformational dynamics of proteins is crucial for elucidating their functional mechanisms. While Molecular Dynamics (MD) simulation enables detailed time evolution of protein motion, its computational toll hinders its use in…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity…

The inapplicability of amino acid covariation methods to small protein families has limited their use for structural annotation of whole genomes. Recently, deep learning has shown promise in allowing accurate residue-residue contact…

This paper focuses on estimating probability distributions over the set of 3D rotations ($SO(3)$) using deep neural networks. Learning to regress models to the set of rotations is inherently difficult due to differences in topology between…

Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between the Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network…

Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete…

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward…

We present the next-to-next-to-leading order (NNLO) calculation of quark quasi parton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full…

Iterative approximation methods using backpropagation enable the optimization of neural networks, but they remain computationally expensive, especially when used at scale. This paper presents an efficient alternative for optimizing neural…

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through…

Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…