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It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of…

Visual-inertial systems rely on precise calibrations of both camera intrinsics and inter-sensor extrinsics, which typically require manually performing complex motions in front of a calibration target. In this work we present a novel…

Dropout is a widely used regularization technique in deep learning, but its effects are typically realized through stochastic masking rather than explicit optimization objectives. We propose a deterministic formulation that expresses…

Learning-based 3D reconstruction methods have shown impressive results. However, most methods require 3D supervision which is often hard to obtain for real-world datasets. Recently, several works have proposed differentiable rendering…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for…

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep…

In this paper, we propose a learning-based framework for non-rigid shape registration without correspondence supervision. Traditional shape registration techniques typically rely on correspondences induced by extrinsic proximity, therefore…

In this article, we study curvature-like feature value of data sets in Euclidean spaces. First, we formulate such curvature functions with desirable properties under the manifold hypothesis. Then we make a test property for the validity of…

While generative models have become increasingly prevalent across various domains, fundamental concerns regarding their reliability persist. A crucial yet understudied aspect of these models is the uncertainty quantification surrounding…

Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available.…

Ultrasound elasticity images which enable the visualization of quantitative maps of tissue stiffness can be reconstructed by solving an inverse problem. Classical model-based approaches for ultrasound elastography use deterministic finite…

We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

This article presents an innovative study in exploring, evaluating, and implementing deep learning architectures for the calibration of multi-modal sensor systems. The focus behind this is to leverage the use of sensor fusion to achieve…

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…