Related papers: Designing a general library for convolutions
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
In this paper, we consider a general notion of convolution. Let $D$ be a finite domain and let $D^n$ be the set of $n$-length vectors (tuples) of $D$. Let $f : D \times D \to D$ be a function and let $\oplus_f$ be a coordinate-wise…
Meta-learning researchers face two fundamental issues in their empirical work: prototyping and reproducibility. Researchers are prone to make mistakes when prototyping new algorithms and tasks because modern meta-learning methods rely on…
We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the…
In product design, a decomposition of the overall product function into a set of smaller, interacting functions is usually considered a crucial first step for any computer-supported design tool. Here, we propose a new approach for the…
Simulated evolution of biological networks can be used to generate functional networks as well as investigate hypotheses regarding natural evolution. A handful of studies have shown how simulated evolution can be used for studying the…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formalize is a Taylor theorem for functions of several variables,…
Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of…
The democratization of Data Mining has been widely successful thanks in part to powerful and easy-to-use Machine Learning libraries. These libraries have been particularly tailored to tackle Supervised Learning. However, strong supervision…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
Following in the footsteps of the success of Mathlib - the centralised library of formalised mathematics in Lean - CSLib is a rapidly-growing centralised library of formalised computer science and software. In this paper, we present its…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
Advances in Large Language Models (LLMs) have spurred a wave of LLM library learning systems for mathematical reasoning. These systems aim to learn a reusable library of tools, such as formal Isabelle lemmas or Python programs that are…
Mean-field games (MFGs) are limiting models to approximate $N$-player games, with a number of applications. Despite the ever-growing numerical literature on computation of MFGs, there is no library that allows researchers and practitioners…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
Conan is a C++ library created for the accurate and efficient modelling, inference and analysis of complex networks. It implements the generation and modification of graphs according to several published models, as well as the unexpensive…