Related papers: Adaptive Patching for Tensor Train Computations
We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…
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.…
A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the {\em tensor train incremental core expansion} (TT-ICE) improves upon the current…
Specialized accelerators for tensor-operations, such as blocked-matrix operations and multi-dimensional convolutions, have been emerged as powerful architecture choices for high-performance Deep-Learning computing. The rapid development of…
The qubit mapping problem (QMP) focuses on the mapping and routing of qubits in quantum circuits so that the strict connectivity constraints imposed by near-term quantum hardware are satisfied. QMP is a pivotal task for quantum circuit…
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.…
This paper studies the low-rank property of the inverse of a class of large-scale structured matrices in the tensor-train (TT) format, which is typically discretized from differential operators. An interesting question that we are concerned…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…
The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance…
While the Transformer architecture has become ubiquitous in the machine learning field, its adaptation to 3D shape recognition is non-trivial. Due to its quadratic computational complexity, the self-attention operator quickly becomes…
Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of…
We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured partitioning of the spacetime domain into tent-shaped regions…
Fine-tuning large pre-trained language models on various downstream tasks with whole parameters is prohibitively expensive. Hence, Parameter-efficient fine-tuning has attracted attention that only optimizes a few task-specific parameters…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
Adversarial patches in computer vision can be used, to fool deep neural networks and manipulate their decision-making process. One of the most prominent examples of adversarial patches are evasion attacks for object detectors. By covering…
Quadrotor control policies can be trained with high performance using the exact gradients of the rewards to directly optimize policy parameters via backpropagation-through-time (BPTT). However, designing a fully differentiable reward…