Related papers: Bond-weighting method for the Grassmann tensor ren…
The support vector machines (SVM) is a powerful classifier used for binary classification to improve the prediction accuracy. However, the non-differentiability of the SVM hinge loss function can lead to computational difficulties in high…
We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are…
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…
In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite $N$ corrections…
We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the…
Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
The lattice QCD simulation with the lattice chiral symmetry is very attractive, however, it is difficult to maintain the symmetry at a modest numerical computation cost. A candidate to reduce the computational cost during the configuration…
Binary neural networks (BNNs) have received ever-increasing popularity for their great capability of reducing storage burden as well as quickening inference time. However, there is a severe performance drop compared with real-valued…
Over-fitting-based image compression requires weights compactness for compression and fast convergence for practical use, posing challenges for deep convolutional neural networks (CNNs) based methods. This paper presents a simple…
We compare different versions of a bosonic description for systems of interacting fermions, with particular emphasis on the free energy functional. The bosonic effective action makes the issue of symmetries particularly transparent and we…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…
We propose a new parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion…
Random bond Ising systems on a general hierarchical lattice are considered. Interesting inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These lead to upper bounds on the…
We reformulate the nonperturbative functional renormalization group for the random field Ising model in a superfield formalism, extending the supersymmetric description of the critical behavior of the system first proposed by Parisi and…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
This paper is on improving the training of binary neural networks in which both activations and weights are binary. While prior methods for neural network binarization binarize each filter independently, we propose to instead parametrize…
The bottleneck part of anisotropic tensor renormalization group (ATRG) is a swapping bonds part which consists of a contraction of two tensors and a partial singular value decomposition of a matrix, and their computational costs are…
While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized…
Tensorial Convolutional Neural Networks (TCNNs) have attracted much research attention for their power in reducing model parameters or enhancing the generalization ability. However, exploration of TCNNs is hindered even from weight…