Related papers: Geometric Optimisation on Manifolds with Applicati…

We introduce gvnn, a neural network library in Torch aimed towards bridging the gap between classic geometric computer vision and deep learning. Inspired by the recent success of Spatial Transformer Networks, we propose several new layers…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric…

Geometric learning has emerged as a powerful paradigm for modeling non-Euclidean data, especially graph-structured ones, with applications spanning social networks, molecular structures, knowledge graphs, and recommender systems. While…

Python has become the de-facto language for training deep neural networks, coupling a large suite of scientific computing libraries with efficient libraries for tensor computation such as PyTorch or TensorFlow. However, when models are used…

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold…

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to…

Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such functions. Our approach extends approximation techniques for…

Motivated by the growing demand for low-precision arithmetic in computational science, we exploit lower-precision emulation in Python -- widely regarded as the dominant programming language for numerical analysis and machine learning.…

Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…

This document is a follow-up to our previous paper dedicated to a vectorized derivation of backpropagation in CNNs. Following the same principles and notations already put in place there, we now focus on transformer-based…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Graph neural networks (GNNs) have recently emerged as a promising learning paradigm in learning graph-structured data and have demonstrated wide success across various domains such as recommendation systems, social networks, and electronic…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…

In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…

Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such…

Recent progress in LLM-driven algorithm discovery, exemplified by DeepMind's AlphaEvolve, has produced new best-known solutions for a range of hard geometric and combinatorial problems. This raises a natural question: to what extent can…