Related papers: Renormalization of tensor networks using graph ind…
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…
We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. This method makes use of the strong disorder…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…
Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can…
We propose a general procedure for extracting the running coupling constants of the underlying field theory of a given classical statistical model on a two-dimensional lattice, combining tensor network renormalization (TNR) and the…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with…
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the…
Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To…
Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
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…
In this paper, we focus on the interpretability of deep neural network. Our work is motivated by the renormalization group (RG) in statistical mechanics. RG plays the role of a bridge connecting microscopical properties and macroscopic…
The standard nonperturbative approaches of renormalization group for tensor models are generally focused on a purely local potential approximation (i.e. involving only generalized traces and product of them) and are showed to strongly…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…