Related papers: On Explicit Curvature Regularization in Deep Gener…

Current traditional methods for LiDAR-camera extrinsics estimation depend on offline targets and human efforts, while learning-based approaches resort to iterative refinement for calibration results, posing constraints on their…

We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

We introduce a novel concept of coarse extrinsic curvature for Riemannian submanifolds, inspired by Ollivier's notion of coarse Ricci curvature. This curvature is derived from the Wasserstein 1-distance between probability measures…

There has been significant recent interest in the use of deep learning for regularizing imaging inverse problems. Most work in the area has focused on regularization imposed implicitly by convolutional neural networks (CNNs) pre-trained for…

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…

Several works have shown that the regularization mechanisms underlying deep neural networks' generalization performances are still poorly understood. In this paper, we hypothesize that deep neural networks are regularized through their…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient,…

Visual-inertial sensors have a wide range of applications in robotics. However, good performance often requires different sophisticated motion routines to accurately calibrate camera intrinsics and inter-sensor extrinsics. This work…

Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications,…

Autonomous vehicles and robots need to operate over a wide variety of scenarios in order to complete tasks efficiently and safely. Multi-camera self-supervised monocular depth estimation from videos is a promising way to reason about the…

Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned…

The problem of UV divergences in QFT has long been a fundamental challenge. Standard regularization techniques modify high-energy behavior to ensure well-defined integrals. However, these approaches often introduce unphysical parameters,…

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…

One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…

In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…