Related papers: TLib: A Flexible C++ Tensor Framework for Numerica…
Deep learning (DL) compilers rely on cost models and auto-tuning to optimize tensor programs for target hardware. However, existing approaches depend on large offline datasets, incurring high collection costs and offering suboptimal…
Tensor processing infrastructures such as deep learning frameworks and specialized hardware accelerators have revolutionized how computationally intensive code from domains such as deep learning and image processing is executed and…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
We consider the problem of transposing tensors of arbitrary dimension and describe TTC, an open source domain-specific parallel compiler. TTC generates optimized parallel C++/CUDA C code that achieves a significant fraction of the system's…
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by…
Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…
Modern ConvNets continue to achieve state-of-the-art results over a vast array of vision and image classification tasks, but at the cost of increasing parameters. One strategy for compactifying a network without sacrificing much expressive…
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the…
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…
Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks…
We initiate an open-source library for the efficient analysis of temporal graphs. We consider one of the standard models of dynamic networks in which each edge has a discrete timestamp and transition time. Recently there has been a massive…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
The success and popularity of deep learning is on the rise, partially due to powerful deep learning frameworks such as TensorFlow and PyTorch that make it easier to develop deep learning models. However, these libraries also come with steep…
From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…
\noindent Model building in $\mathsf{SO(10)}$, which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves…