Related papers: Tensor renormalization group in bosonic field theo…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…
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…
Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2),…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
We discuss the free-energy density of bosonic and fermionic theories possessing strongly coupled critical points in D=3. We construct a stationary renormalization group trajectory which interpolates between the free massless theory of N…
In usual (non-stochastic) tensor network calculations, the truncated singular value decomposition (SVD) is often used for approximating a tensor, and it causes systematic errors. By introducing stochastic noise in the approximation,…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
We introduce a new numerical method for the solution of self-consistent equations in the cluster mean-field theory. The method uses the density matrix renormalization group method to solve the associated cluster problem. We obtain an…
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group…
We describe the most general local, Lorentz-invariant, effective field theory of scalars, fermions and gauge bosons up to mass dimension 6. We first obtain both a Green and a physical basis for such an effective theory, together with the…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…
The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…
By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…