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Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
Metaheuristics are popularly used in various fields, and they have attracted much attention in the scientific and industrial communities. In recent years, the number of new metaheuristic names has been continuously growing. Generally, the…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
In this paper, we propose an approach to improve few-shot classification performance using a composite rotation based auxiliary task. Few-shot classification methods aim to produce neural networks that perform well for classes with a large…
We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…
Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…
The asymmetric objective function is proposed as an alternative to Huber objective function to model skewness and obtain robust estimators for the location, scale and skewness parameters. The robustness and asymptotic properties of the…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…
We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and…
Let $m$ be an even positive integer. A Boolean bent function $f$ on $\GF{m-1} \times \GF {}$ is called a \emph{cyclic bent function} if for any $a\neq b\in \GF {m-1}$ and $\epsilon \in \GF{}$, $f(ax_1,x_2)+f(bx_1,x_2+\epsilon)$ is always…