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Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that…
Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and…
Most Gaussian Splatting techniques that provide a 3D semantic representation of the scene do not optimize the underlying 3D geometry, making object-level editing or asset extraction challenging. Recent methods, such as COBGS, Trace3D,…
We propose an online planning approach for racing that generates the time-optimal trajectory for the upcoming track section. The resulting trajectory takes the current vehicle state, effects caused by \acl{3D} track geometries, and speed…
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…
In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into…
The latest sheet stamping processes enable efficient manufacturing of complex shape structural components that have high stiffness to weight ratios, but these processes can introduce defects. To assist component design for stamping…
We propose a robust method for estimating dynamic 3D curvilinear branching structure from monocular images. While 3D reconstruction from images has been widely studied, estimating thin structure has received less attention. This problem…
3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time, high-resolution novel view synthesis. By representing scenes as a mixture of Gaussian primitives, 3DGS leverages GPU rasterization pipelines for efficient…
In the film and gaming industries, achieving a realistic hair appearance typically involves the use of strands originating from the scalp. However, reconstructing these strands from observed surface images of hair presents significant…
Single-frame sports field registration often serves as the foundation for extracting 3D information from broadcast videos, enabling applications related to sports analytics, refereeing, or fan engagement. As sports fields have rigorous…
3D scene reconstruction is fundamental for spatial intelligence applications such as AR, robotics, and digital twins. Traditional multi-view stereo struggles with sparse viewpoints or low-texture regions, while neural rendering approaches,…
We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems. Our technique represents the natural gradient direction as a…
Recent advances in 3D Gaussian Splatting (3DGS) have focused on accelerating optimization while preserving reconstruction quality. However, many proposed methods entangle implementation-level improvements with fundamental algorithmic…
We propose a methodology for lidar super-resolution with ground vehicles driving on roadways, which relies completely on a driving simulator to enhance, via deep learning, the apparent resolution of a physical lidar. To increase the…
There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for non-convex empirical risk minimization problems over a peer-to-peer network of nodes, which is in sharp contrast to the existing DSGT only for convex…
3D Gaussian Splatting (3DGS) has recently unlocked real-time, high-fidelity novel view synthesis by representing scenes using explicit 3D primitives. However, traditional methods often require millions of Gaussians to capture complex…
Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…