Related papers: Quaternionic Step Derivative: Machine Precision Di…
The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…
Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…
Conventional Convolutional neural networks (CNN) are trained on large domain datasets and are hence typically over-represented and inefficient in limited class applications. An efficient way to convert such large many-class pre-trained…
Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and…
Part-level representations are essential for robust person re-identification. However, common errors that arise during pedestrian detection frequently result in severe misalignment problems for body parts, which degrade the quality of part…
This paper presents an efficient object detection method from satellite imagery. Among a number of machine learning algorithms, we proposed a combination of two convolutional neural networks (CNN) aimed at high precision and high recall,…
It has long been known that differential forms on complex manifolds can be decomposed under the action of the complex structure to give the Dolbeault complex. This paper presents an analogous double complex for quaternionic manifolds using…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
A key problem in automatic analysis and understanding of scientific papers is to extract semantic information from non-textual paper components like figures, diagrams, tables, etc. Much of this work requires a very first preprocessing step:…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…
One of the most challenging tasks in microarray image analysis is spot segmentation. A solution to this problem is to provide an algorithm than can be used to find any spot within the microarray image. Circular Hough Transformation (CHT) is…
A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations.…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…
A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information in gradient based training. Forward pass calculates not only…
A heuristic formula for 5-point approximation of the first derivative of an unknown function whose values are measured with an error at unequally spaced points is proposed. The derivative at a given point is calculated using the effective…
We introduce Combinatory Homomorphic Automatic Differentiation (CHAD), a principled, pure, provably correct define-then-run method for performing forward- and reverse-mode automatic differentiation (AD) on programming languages with…
This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…