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Deep Generative Models (DGMs) have found application in computer vision for generating adversarial examples to test the robustness of machine learning (ML) systems. Extending these adversarial techniques to tabular ML presents unique…
Recently, large-scale language-image generative models have gained widespread attention and many works have utilized generated data from these models to further enhance the performance of perception tasks. However, not all generated data…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We…
In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are…
GPUs are dedicated processors used for complex calculations and simulations and they can be effectively used for tropical algebra computations. Tropical algebra is based on max-plus algebra and min-plus algebra. In this paper we proposed…
Graph convolutional networks (GCNs) are widely used in graph-based applications such as graph classification and segmentation. However, current GCNs have limitations on implementation such as network architectures due to their irregular…
We propose GALA, a novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern,…
Over the past twenty years, artificial Gene Regulatory Networks (GRNs) have shown their capacity to solve real-world problems in various domains such as agent control, signal processing and artificial life experiments. They have also…
Deep generative models learned through adversarial training have become increasingly popular for their ability to generate naturalistic image textures. However, aside from their texture, the visual appearance of objects is significantly…
Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…
The application of operator overloading algorithmic differentiation (AD) to computer programs in order to compute the derivative is quite common. But, the replacement of the underlying computational floating point type with the specialized…
Deep learning software demands reliability and performance. However, many of the existing deep learning frameworks are software libraries that act as an unsafe DSL in Python and a computation graph interpreter. We present DLVM, a design and…
Most of the literature of computational geometry concerns geometric properties of sets of static points. M.J. Atallah introduced dynamic computational geometry, concerned with both momentary and long-term geometric properties of sets of…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
Deep Learning has made a great progress for these years. However, it is still difficult to master the implement of various models because different researchers may release their code based on different frameworks or interfaces. In this…
Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…