Related papers: Symbolic Tensor Calculus -- Functional and Dynamic…
The high-energy physics community is investigating the potential of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to enhance physics sensitivity while still meeting data processing time constraints. In…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
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…
This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary…
The CLEARS (Computational Linguistics Education and Research for Semantics) tool provides a graphical interface allowing interactive construction of semantic representations in a variety of different formalisms, and using several…
Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained…
The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known…
We present a compositional semantics for various types of polar questions and wh-questions within the framework of Combinatory Categorial Grammar (CCG). To assess the explanatory power of our proposed analysis, we introduce a…
The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the…
Symbolic Regression (SR) is a type of regression analysis to automatically find the mathematical expression that best fits the data. Currently, SR still basically relies on various searching strategies so that a sample-specific model is…
We describe software for symbolic computations that we developed in order to find Hamiltonian operators for Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equations, and verify their compatibility. The computation involves nonlocal…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
Log-linear models provide a statistically sound framework for Stochastic ``Unification-Based'' Grammars (SUBGs) and stochastic versions of other kinds of grammars. We describe two computationally-tractable ways of estimating the parameters…