Related papers: Tensor Network Rewriting Strategies for Satisfiabi…
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…
Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…
The unification of neural and symbolic approaches to artificial intelligence remains a central open challenge. In this work, we introduce a tensor network formalism, which captures sparsity principles originating in the different approaches…
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Quantum circuit simulation is a challenging computational problem crucial for quantum computing research and development. The predominant approaches in this area center on tensor networks, prized for their better concurrency and less…
The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…
The problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the 2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly to the…
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. 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 prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar…