Related papers: A gradient system on the quantum information space…
Kakade's natural policy gradient method has been studied extensively in recent years, showing linear convergence with and without regularization. We study another natural gradient method based on the Fisher information matrix of the…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…
Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
Recent results suggest that flow-based algorithms may provide efficient sampling of field distributions for lattice field theory applications, such as studies of quantum chromodynamics and the Schwinger model. In this work, we provide a…
Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free linear quadratic regulator (LQR), and linear feedforward…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
Diffusion Models (DMs) have impressive capabilities among generation models, but are limited to slower inference speeds and higher computational costs. Previous works utilize one-shot structure pruning to derive lightweight DMs from…
Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits…
Gradient estimation is a central challenge in training parameterized quantum circuits (PQCs) for hybrid quantum-classical optimization and learning problems. This difficulty arises from several factors, including the exponential…