Related papers: Pytearcat: PYthon TEnsor AlgebRa calCulATor
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and…
Sparse linear algebra is a cornerstone of many scientific computing and machine learning applications. Python has become a popular choice for these applications due to its simplicity and ease of use. Yet high performance sparse kernels in…
RTL simulation on CPUs remains a persistent bottleneck in hardware design. State-of-the-art simulators embed the circuit directly into the simulation binary, resulting in long compilation times and execution that is fundamentally CPU…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…
HOTTBOX is a Python library for exploratory analysis and visualisation of multi-dimensional arrays of data, also known as tensors. The library includes methods ranging from standard multi-way operations and data manipulation through to…
Since Lorenz's seminal work on a simplified weather model, the numerical analysis of nonlinear dynamical systems has become one of the main subjects of research in physics. Despite of that, there remains a need for accessible, efficient,…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
We present an automatic static analyzer PyTea that detects tensor-shape errors in PyTorch code. The tensor-shape error is critical in the deep neural net code; much of the training cost and intermediate results are to be lost once a tensor…
We introduce Texar, an open-source toolkit aiming to support the broad set of text generation tasks that transform any inputs into natural language, such as machine translation, summarization, dialog, content manipulation, and so forth.…
Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an…
GRTensorJ - Books is an active interface to a small part of the computer algebra systems GRTensorII (for Maple) and GRTensorM (for Mathematica) with the specific intent of providing students of General Relativity with an advanced…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
Condensed matter compounds typically form crystals, which break the rotational and translational invariance of space but remain invariant under a discrete set of symmetry operations. Understanding the effects allowed by this symmetry…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
Spreadsheets are widely used in various fields to do large numerical analysis. While several companies have relied on spreadsheets for decades, data scientists are going in the direction of using scientific programming languages such as…
BasisGen is a Python package for the automatic generation of bases of operators in effective field theories. It accepts any semisimple symmetry group and fields in any of its finite dimensional irreducible representations. It takes into…
The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, The tensor t-function: a definition for functions of third-order tensors, Numer. Linear…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…