We revisit the asymptotically optimal quantum linear system solver of childs, kothari, and somma from the perspective of convex optimization, and in particular gradient descent-type algorithms.
We first show how the asymptotically optimal quantum linear system solver of childs, kothari, and somma is related to the gradient descentalgorithm on the convex function their linear system solver is based on a truncation in the chebyshev basis of the polynomial (in that maps the initial solution to the iterate in the basic gradient descent algorithm).
Many machine learning problems encode their data as a matrix with a possibly very large number of rows and columns.
In several applications like neuroscience, image compression or deep reinforcement learning, the principalsubspace of such a matrix provides a useful, low-dimensional representation of individual data.
We develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points.
The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updatedtowards the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution.
We investigate uniform boundedness properties of iterates and function values along the trajectories of the stochastic gradient descent algorithm and its important momentum variant.
Under smoothness and of the loss function, we show that broad families of step-sizes, including the widely used step-decay and cosine with (or without) restart step-sizes, result in uniformlybounded iterates and function values.
We study the convergence properties of the deterministic score-based method to sample from named kernel stein discretization (ksd), which uses a set of particles to approximate a target probability distribution on known up to a normalization constant.
Remarkably, owing to a tractable loss function, ksddescent can leverage robust parameter-free optimization schemes such as the l-bfgs.