Related papers: A gradient system on the quantum information space…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
Quantum natural gradient has emerged as a superior minimisation technique in quantum variational algorithms. Classically simulating the algorithm running on near-future quantum hardware is paramount in its study, as it is for all…
Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a…
We propose a method for estimating the Fisher score--the gradient of the log-likelihood with respect to model parameters--using score matching. By introducing a latent parameter model, we show that the Fisher score can be learned by…
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…
We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresponding gradient flow on parameter space can be written as a…
Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so…
Otto's (2001) Wasserstein gradient flow of the exclusive KL divergence functional provides a powerful and mathematically principled perspective for analyzing learning and inference algorithms. In contrast, algorithms for the inclusive KL…
Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution…
This study established a quantum-classical hybrid framework that integrates quantum computing paradigm with meshfree finite particle method. By harnessing quantum superposition and entanglement, it hybridized the critical computational…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distributions with finite second moment. It derives a class of…
This paper deals with the geometric numerical integration of gradient flow and its application to optimization. Gradient flows often appear as model equations of various physical phenomena, and their dissipation laws are essential.…
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that…
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…
We describe a gradient flow structure for the inviscid Langmuir layer Stokesian subfluid model introduced recently by Alexander et al [1].
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…
The expectation that quantum computation might bring performance advantages in machine learning algorithms motivates the work on the quantum versions of artificial neural networks. In this study, we analyze the learning dynamics of a…
A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum…