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Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
Despite the potential of neural scene representations to effectively compress 3D scalar fields at high reconstruction quality, the computational complexity of the training and data reconstruction step using scene representation networks…
Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the…
An artificial neural network (ANN) is a numerical method used to solve complex classification problems. Due to its high classification power, the ANN method often outperforms other classification methods in terms of accuracy. However, an…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different…
This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…
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…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical and quantum systems in thermal equilibrium. At every step of the iterative…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
We study the three-dimensional $SU(2)$ principal chiral model (PCM) using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
Traditional tensor decomposition methods, e.g., two dimensional principal component analysis and two dimensional singular value decomposition, that minimize mean square errors, are sensitive to outliers. To overcome this problem, in this…
Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the…
We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…