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Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

The spinal angle is an important indicator of body balance. It is important to restore the 3D shape of the human body and estimate the spine center line. Existing mul-ti-image-based body restoration methods require expensive equipment and…

Widespread development of driverless vehicles has led to the formation of autonomous racing, where technological development is accelerated by the high speeds and competitive environment of motorsport. A particular challenge for an…

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

We propose a novel optimization-based paradigm for 3D human model fitting on images and scans. In contrast to existing approaches that directly regress the parameters of a low-dimensional statistical body model (e.g. SMPL) from input…

Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…

3D Gaussian Splatting (3DGS) has emerged as a promising 3D reconstruction technique. The traditional 3DGS training pipeline follows three sequential steps: Gaussian densification, Gaussian projection, and color splatting. Despite its…

We consider the problem of finding an optimal 3D road trajectory between two points on a terrain with variable elevation. Unlike common heuristic pathfinding methods, we propose a rigorous framework based on the calculus of variations,…

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA…

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point…

Projected Gradient Descent (PGD) is a strong and widely used first-order adversarial attack, yet its computational cost scales poorly, as all training samples undergo identical iterative inner-loop optimization despite contributing…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Deep learning models achieve state-of-the-art performance across domains but face scalability challenges in real-time or resource-constrained scenarios. To address this, we propose Correlation of Loss Differences (CLD), a simple and…

There introduce Particle Optimized Gradient Descent (POGD), an algorithm based on the gradient descent but integrates the particle swarm optimization (PSO) principle to achieve the iteration. From the experiments, this algorithm has…

In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…

Trajectory optimization (TO) aims to find a sequence of valid states while minimizing costs. However, its fine validation process is often costly due to computationally expensive collision searches, otherwise coarse searches lower the…

We propose a method to enhance 3D Gaussian Splatting (3DGS)~\cite{Kerbl2023}, addressing challenges in initialization, optimization, and density control. Gaussian Splatting is an alternative for rendering realistic images while supporting…

Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…