Related papers: HotSpot: Signed Distance Function Optimization wit…

This paper studies the optimal placement of ceiling-mounted metasurfaces (MTSs) to help focus the wireless signal beam onto the target receiver, as inspired by the theatre spotlight. We assume that a total of $M$ MTSs are deployed, and that…

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural…

Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…

Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

This paper addresses the challenges of optimally placing a finite number of sensors to detect Poisson-distributed targets in a bounded domain. We seek to rigorously account for uncertainty in the target arrival model throughout the problem.…

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential decay of eigenvalues associated with the forward problems.…

The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

Implicit reconstruction of ESDF (Euclidean Signed Distance Field) involves training a neural network to regress the signed distance from any point to the nearest obstacle, which has the advantages of lightweight storage and continuous…

Discrete stochastic optimization considers the problem of minimizing (or maximizing) loss functions defined on discrete sets, where only noisy measurements of the loss functions are available. The discrete stochastic optimization problem is…

We proposed a generalized method, NeuralSSD, for reconstructing a 3D implicit surface from the widely-available point cloud data. NeuralSSD is a solver-based on the neural Galerkin method, aimed at reconstructing higher-quality and accurate…

We consider the problem of learning a loss function which, when minimized over a training dataset, yields a model that approximately minimizes a validation error metric. Though learning an optimal loss function is NP-hard, we present an…

The loss function is crucial to machine learning, especially in supervised learning frameworks. It is a fundamental component that controls the behavior and general efficacy of learning algorithms. However, despite their widespread use,…

Accurate and dense mapping in large-scale environments is essential for various robot applications. Recently, implicit neural signed distance fields (SDFs) have shown promising advances in this task. However, most existing approaches employ…

Geodesic distances play a fundamental role in robotics, as they efficiently encode global geometric information of the domain. Recent methods use neural networks to approximate geodesic distances by solving the Eikonal equation through…