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3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussian-based representation and introduces an approximated volumetric rendering, achieving very fast rendering speed and promising…

We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…

Metasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global…

While 3D Gaussian Splatting (3DGS) enables high-quality, real-time rendering for bounded scenes, its extension to large-scale urban environments gives rise to critical challenges in terms of geometric consistency, memory efficiency, and…

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…

3D Gaussian Splatting (3D-GS) has emerged as an efficient 3D representation and a promising foundation for semantic tasks like segmentation. However, existing 3D-GS-based segmentation methods typically rely on high-dimensional category…

Accurate 3D reconstruction of dynamic surgical scenes from endoscopic video is essential for robotic-assisted surgery. While recent 3D Gaussian Splatting methods have shown promise in achieving high-quality reconstructions with fast…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

Adversarial attacks present a critical challenge to deep neural networks' robustness, particularly in transfer scenarios across different model architectures. However, the transferability of adversarial attacks faces a fundamental dilemma…

Neural image representations have emerged as a promising approach for encoding and rendering visual data. Combined with learning-based workflows, they demonstrate impressive trade-offs between visual fidelity and memory footprint. Existing…

High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is…

Reconstructing objects from posed images is a crucial and complex task in computer graphics and computer vision. While NeRF-based neural reconstruction methods have exhibited impressive reconstruction ability, they tend to be…

In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…

The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…

We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…

Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search…

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…