Related papers: Tensor network subspace identification of polynomi…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that…
We present a systematic study of Tensor Network (TN) models $\unicode{x2013}$ Matrix Product States (MPS) and Tree Tensor Networks (TTN) $\unicode{x2013}$ for real-time jet tagging in high-energy physics, with a focus on low-latency…
We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…
With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper…
Data mining practitioners are facing challenges from data with network structure. In this paper, we address a specific class of global-state networks which comprises of a set of network instances sharing a similar structure yet having…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…