Related papers: GenTT: Generate Vectorized Codes for General Tenso…
This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…
Current AI training infrastructure is dominated by single instruction multiple data (SIMD) and systolic array architectures, such as Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs), that excel at accelerating parallel…
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Tensor is the most basic and essential data structure of nowadays artificial intelligence (AI) system. The natural properties of Tensor, especially the memory-continuity and slice-independence, make it feasible for training system to…
We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses…
Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for…
We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the…
SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application…
Existing large language model-based code generation pipelines typically use beam search or sampling algorithms during the decoding process. Although the programs they generate achieve high token-matching-based scores, they often fail to…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Tensor network codes enable structured construction and manipulation of stabilizer codes out of small seed codes. Here, we apply reinforcement learning to tensor network code geometries and demonstrate how optimal stabilizer codes can be…
Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and…
In recent years, a great deal of attention has been paid to the Transformer network for speech recognition tasks due to its excellent model performance. However, the Transformer network always involves heavy computation and large number of…
In software, text is often represented using Unicode formats (UTF-8 and UTF-16). We frequently have to convert text from one format to the other, a process called transcoding. Popular transcoding functions are slower than state-of-the-art…
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…