Related papers: Fine-Grained Tensor Network Methods
The observation, design and analysis of mesh-like networks in bionics, polymer physics and biological systems has brought forward an extensive catalog of fascinating structures of which a subgroup share a particular, yet critically under…
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…
Designing superconducting quantum hardware requires simulation tools that can account for various deviations from ideal scenarios. This, in turn, requires approaches that automatically detect certain structures and leverage them to make the…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…
We present an unconstrained tree tensor network approach to the study of lattice gauge theories in two spatial dimensions showing how to perform numerical simulations of theories in presence of fermionic matter and four-body magnetic terms,…
Magnitude Pruning is a staple lightweight network design method which seeks to remove connections with the smallest magnitude. This process is either achieved in a structured or unstructured manner. While structured pruning allows reaching…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
Lattices are important as models for the node locations in wireless networks for two main reasons: (1) When network designers have control over the placement of the nodes, they often prefer a regular arrangement in a lattice for coverage…
We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…
We propose a novel fine-grained cross-view localization method that estimates the 3 Degrees of Freedom pose of a ground-level image in an aerial image of the surroundings by matching fine-grained features between the two images. The pose is…
We present a graph-based deep learning framework for predicting the magnetic properties of quasi-one-dimensional Ising spin systems. The lattice geometry is encoded as a graph and processed by a graph neural network (GNN) followed by fully…
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…
We present a novel network pruning algorithm called Dynamic Sparse Training that can jointly find the optimal network parameters and sparse network structure in a unified optimization process with trainable pruning thresholds. These…
Tensor network algorithms have proven to be very powerful tools for studying one- and two-dimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because…
Modern deep neural networks rely on overparameterization to achieve state-of-the-art generalization. But overparameterized models are computationally expensive. Network pruning is often employed to obtain less demanding models for…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum…
We construct an algorithm to simulate imaginary time evolution of translationally invariant spin systems with local interactions on an infinite, symmetric tree. We describe the state by symmetric iPEPS and use translation-invariant…
An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as non-binary belief propagation on associated TGs;…