Related papers: Geometric Optimisation on Manifolds with Applicati…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be…

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…

Software packages like TensorFlow and PyTorch are designed to support linear algebra operations, and their speed and usability determine their success. However, by prioritising speed, they often neglect memory requirements. As a…

We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs…

Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…

Automatic differentiation frameworks are optimized for exactly one thing: computing the average mini-batch gradient. Yet, other quantities such as the variance of the mini-batch gradients or many approximations to the Hessian can, in…

Memory is a limiting resource for many deep learning tasks. Beside the neural network weights, one main memory consumer is the computation graph built up by automatic differentiation (AD) for backpropagation. We observe that PyTorch's…

In this work, we study optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps…

Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the…

We test the efficiency of applying Geometric Deep Learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use Graph Neural…

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…

Data augmentation is a key technique for addressing the challenge of limited datasets, which have become a major component in the training procedures of image processing. Techniques such as geometric transformations and color space…

We present Kaolin, a PyTorch library aiming to accelerate 3D deep learning research. Kaolin provides efficient implementations of differentiable 3D modules for use in deep learning systems. With functionality to load and preprocess several…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

Combinatorial optimization problems are prevalent across a wide variety of domains. These problems are often nuanced, their optimal solutions might not be efficiently obtainable, and they may require lots of time and compute resources to…

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite…

Local execution of AI on edge devices is important for low latency and offline operation. However, deploying models on diverse hardware remains fragmented, often requiring model conversion or complete reimplementation outside the PyTorch…