Related papers: Newton's Algorithm as a Gradient Flow: A Geometric…

This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a…

Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

We propose a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph. The algorithm employs an inexact, preconditioned Newton…

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable…

We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…

Efficient approximation of geodesics is crucial for practical algorithms on manifolds. Here we introduce a class of retractions on submanifolds, induced by a foliation of the ambient manifold. They match the projective retraction to the…

Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…

We propose a simple recursive algorithm that allows the computation of the first- and second-order derivatives with respect to the inputs of an arbitrary deep feed forward neural network (DFNN). The algorithm naturally incorporates the…

In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic…