We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...
We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...
There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...
In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size γ and momentum parameter β that allows u ...
In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of 2-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...
While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...
Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...
In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...
A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...
