Related papers: Global optimization of tensor renormalization grou…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
We study the tensor renormalization group (TRG) in the dimension larger than two as the Higher-order TRG (HOTRG) with the randomized SVD method. The randomized SVD and the detailed discussion on the low order tensor representation, we can…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Due to the rapidly growing scale and heterogeneity of wireless networks, the design of distributed cross-layer optimization algorithms have received significant interest from the networking research community. So far, the standard…
In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image…
We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine the role of GD in inducing implicit regularization for tensor…
This paper proposes network recasting as a general method for network architecture transformation. The primary goal of this method is to accelerate the inference process through the transformation, but there can be many other practical…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…