Related papers: Unconstrained Tree Tensor Network: An adaptive gau…
Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of…
The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…
The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schr\"odinger equation. The associated working equations at play in…
We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We…
Interfaces in three-dimensional many-body systems can exhibit rich phenomena beyond the corresponding bulk properties. In particular, they can fluctuate and give rise to massless low energy degrees of freedom even in the presence of a…
Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
We propose a method to construct a tensor network representation of partition functions without singular value decompositions nor series expansions. The approach is demonstrated for one- and two-dimensional Ising models and we study the…
We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…
As electric grids experience high penetration levels of renewable generation, fundamental changes are required to address real-time situational awareness. This paper uses unique traits of tensors to devise a model-free situational awareness…
Strong Disorder Renormalization for the Random Transverse Field Ising model leads to a complicated topology of surviving clusters as soon as $d>1$. Even if one starts from a Cayley tree, the network of surviving renormalized clusters will…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…