Related papers: Evolution: A Unified Formula for Feature Operators…
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…
Molecular generation and molecular property prediction are both crucial for drug discovery, but they are often developed independently. Inspired by recent studies, which demonstrate that diffusion model, a prominent generative approach, can…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
Feature pyramid has been an efficient method to extract features at different scales. Development over this method mainly focuses on aggregating contextual information at different levels while seldom touching the inter-level correlation in…
Recently, evolutionary multitasking (EMT) has been successfully used in the field of high-dimensional classification. However, the generation of multiple tasks in the existing EMT-based feature selection (FS) methods is relatively simple,…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
Deep neural networks require specific layers to process point clouds, as the scattered and irregular location of 3D points prevents the use of conventional convolutional filters. We introduce the composite layer, a flexible and general…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…
The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Training Deep Convolutional Neural Networks (CNNs) is based on the notion of using multiple kernels and non-linearities in their subsequent activations to extract useful features. The kernels are used as general feature extractors without…
The evolution of cognition is frequently discussed as the evolution of cognitive abilities or the evolution of some neuronal structures in the brain. However, since such traits or abilities are often highly complex, understanding their…
Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and…
Feature selection techniques are essential for high-dimensional data analysis. In the last two decades, their popularity has been fuelled by the increasing availability of high-throughput biomolecular data where high-dimensionality is a…
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…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…
A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these…
We study one dimension in program evolution, namely the evolution of the datatype declarations in a program. To this end, a suite of basic transformation operators is designed. We cover structure-preserving refactorings, but also…