Related papers: Variational boundary based tensor network renormal…
We propose a forward-mode automatic differentiation (AD) framework for tensor renormalization group (TRG) methods. In this approach, evaluating the derivatives of the partition function up to order $k$ increases the matrix-multiplication…
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
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…
In this study, we explore the geometric construction of the Klein bottle and the real projective plane ($\mathrm{RP}^2$) within the framework of tensor networks, focusing on the implementation of crosscap and rainbow boundaries. Previous…
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…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…
Convolutional neural networks are very popular nowadays. Training neural networks is not an easy task. Each convolution corresponds to a structured transformation matrix. In order to help avoid the exploding/vanishing gradient problem, it…
Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture…
This paper proposes a novel binarized weight network (BT) for a resource-efficient neural structure. The proposed model estimates a binary representation of weights by taking into account the approximation error with an additional term.…
We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various…
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…
Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…
Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the…