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Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…
In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
This paper studies the problem of aligning a set of face images of the same individual into a normalized image while removing the outliers like partial occlusion, extreme facial expression as well as significant illumination variation. Our…
The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if…
The generative adversarial network (GAN) exhibits great superiority in the face attribute synthesis task. However, existing methods have very limited effects on the expansion of new attributes. To overcome the limitations of a single…
Generative Adversarial Networks (GAN) have led to the generation of very realistic face images, which have been used in fake social media accounts and other disinformation matters that can generate profound impacts. Therefore, the…
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and…
We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
With the progress in AI-based facial forgery (i.e., deepfake), people are increasingly concerned about its abuse. Albeit effort has been made for training classification (also known as deepfake detection) models to recognize such forgeries,…
Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
While great progress has been made recently in automatic image manipulation, it has been limited to object centric images like faces or structured scene datasets. In this work, we take a step towards general scene-level image editing by…
We present a low-rank transformation approach to compensate for face variations due to changes in visual domains, such as pose and illumination. The key idea is to learn discriminative linear transformations for face images using matrix…
In a recent work, we presented the reduced Jacobian method (RJM) as an extension of Wolfe's reduced gradient method to multicriteria (multiobjective) optimization problems dealing with linear constraints. This approach reveals that using a…
In recent years, Generative Adversarial Networks (GANs) have become a hot topic among researchers and engineers that work with deep learning. It has been a ground-breaking technique which can generate new pieces of content of data in a…
Face attributes are interesting due to their detailed description of human faces. Unlike prior researches working on attribute prediction, we address an inverse and more challenging problem called face attribute manipulation which aims at…