Related papers: Geometric Optimisation on Manifolds with Applicati…

Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…

PyG (PyTorch Geometric) has evolved significantly since its initial release, establishing itself as a leading framework for Graph Neural Networks. In this paper, we present Pyg 2.0 (and its subsequent minor versions), a comprehensive update…

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

TorchOptics is an open-source Python library for differentiable Fourier optics simulations, developed using PyTorch to enable GPU-accelerated tensor computations and automatic differentiation. It provides a comprehensive framework for…

The constant introduction of standardized benchmarks in the literature has helped accelerating the recent advances in meta-learning research. They offer a way to get a fair comparison between different algorithms, and the wide range of…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

Machine learning solutions are very popular in the field of chemoinformatics, where they have numerous applications, such as novel drug discovery or molecular property prediction. Molecular fingerprints are algorithms commonly used for…

Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have…

We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the…

This paper introduces a novel CUDA-enabled PyTorch-based framework designed for the gradient-based optimization of such reconfigurable electromagnetic structures with electrically tunable parameters. Traditional optimization techniques for…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Multi-Task Learning (MTL) seeks to boost statistical power and learning efficiency by discovering structure shared across related tasks. State-of-the-art MTL representation methods, however, usually treat the latent representation matrix as…

With the increasing adoption of graph neural networks (GNNs) in the machine learning community, GPUs have become an essential tool to accelerate GNN training. However, training GNNs on very large graphs that do not fit in GPU memory is…

This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of…

Deep learning has brought significant advancements to X-ray Computed Tomography (CT) reconstruction, offering solutions to challenges arising from modern imaging technologies. These developments benefit from methods that combine classical…

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…