Related papers: Designing a general library for convolutions
Categorization is a fundamental function of minds, with wide ranging implications for the rest of the cognitive system. In humans, categories are shared and communicated between minds, thus requiring explanations at the population level. In…
Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with…
To build a large library of mathematics, it seems more efficient to take advantage of the inherent structure of mathematical theories. Various theory presentation combinators have been proposed, and some have been implemented, in both…
This paper introduces versatile filters to construct efficient convolutional neural networks that are widely used in various visual recognition tasks. Considering the demands of efficient deep learning techniques running on cost-effective…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
We introduce the \prog{Mathematica} package \prog{MT} which can be used to compute, both analytically and numerically, convolutions involving harmonic polylogarithms, polynomials or generalized functions. As applications contributions to…
Today's highly heterogeneous computing landscape places a burden on programmers wanting to achieve high performance on a reasonably broad cross-section of machines. To do so, computations need to be expressed in many different but…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This…
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions,…
We present a library for generic programming in OCaml, adapting some techniques borrowed from other functional languages. The library makes use of three recent additions to OCaml: generalised abstract datatypes are essential to reflect…
In this paper, we showed that the feature map of a convolution layer is equivalent to the unnormalized log posterior of a special kind of Gaussian mixture for image modeling. Then we expanded the model to drive diverse features and proposed…
Establishing accurate morphological measurements of galaxies in a reasonable amount of time for future big-data surveys such as EUCLID, the Large Synoptic Survey Telescope or the Wide Field Infrared Survey Telescope is a challenge. Because…
Machine learning (ML) and artificial intelligence (AI) have become hot topics in many information processing areas, from chatbots to scientific data analysis. At the same time, there is uncertainty about the possibility of extending…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem…
Large Language Models (LLMs) often struggle with code generation tasks involving niche software libraries. Existing code generation techniques with only human-oriented documentation can fail -- even when the LLM has access to web search and…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…