相关论文: Renormalization group on a triad network

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

We investigate the phase transition of the four-dimensional Ising model with two types of tensor network scheme, one is the higher-order tensor renormalization group and the other is the anisotropic tensor renormalization group. The results…

Computer vision tasks are often expected to be executed on compressed images. Classical image compression standards like JPEG 2000 are widely used. However, they do not account for the specific end-task at hand. Motivated by works on…

Tensor rematerialization allows the training of deep neural networks (DNNs) under limited memory budgets by checkpointing the models and recomputing the evicted tensors as needed. However, the existing tensor rematerialization techniques…

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…

In the past years, Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous model size and massive computation cost have become the main obstacle for deployment of such…

We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converting the tensor into a tensor-train rank-1 (TTr1) series via…

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…

Binary neural networks have great resource and computing efficiency, while suffer from long training procedure and non-negligible accuracy drops, when comparing to the full-precision counterparts. In this paper, we propose the composite…

Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…

In dynamical systems reconstruction (DSR) we seek to infer from time series measurements a generative model of the underlying dynamical process. This is a prime objective in any scientific discipline, where we are particularly interested in…

The success of deep learning comes at a tremendous computational and energy cost, and the scalability of training massively overparametrized neural networks is becoming a real barrier to the progress of artificial intelligence (AI). Despite…

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…

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…

Single particle cryo-electron microscopy is a vital tool for 3D characterization of protein structures. A typical workflow involves acquiring projection images of a collection of randomly oriented particles, picking and classifying…

In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can,…

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…

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…