Related papers: Accelerating two-dimensional tensor network optimi…
Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
We present a novel algorithm to reduce tensor compute required by a conditional image generation autoencoder without sacrificing quality of photo-realistic image generation. Our method is device agnostic, and can optimize an autoencoder for…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this paper, we propose a new class of Project Entangled Pair State (PEPS) that incorporates two isometric conditions. This new…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require…
The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves…
A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…
An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice. Here we…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…
Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum…
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…