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A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…
Deep neural networks (DNN) are powerful models for many pattern recognition tasks, yet their high computational complexity and memory requirement limit them to applications on high-performance computing platforms. In this paper, we propose…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…
Point cloud segmentation is one of the most important tasks in computer vision with widespread scientific, industrial, and commercial applications. The research thereof has resulted in many breakthroughs in 3D object and scene…
In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, posessing the maximal possible asymptotic rate of convergence…
X-ray Ptychography is an advanced computational microscopy technique which is delivering exceptionally detailed quantitative imaging of biological and nanotechnology specimens. However coarse parametrisation in propagation distance,…
We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional…
Automated recognition and simplification of fillet features in CAD models is critical for CAE analysis, yet it remains an open challenge. Traditional rule-based methods lack robustness, while existing deep learning models suffer from poor…
Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…
Convolutional Neural Network (CNN) based Deep Learning (DL) has achieved great progress in many real-life applications. Meanwhile, due to the complex model structures against strict latency and memory restriction, the implementation of CNN…
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…
In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method within the context of stochastic differential equations, TSGD is…
Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches…
Decision trees partition the feature space using hard binary thresholds, assigning identical confidence to instances far from a decision boundary and to those directly on it. We introduce ternary decision trees, which augment each split…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
The computational complexity of neural networks for large scale or real-time applications necessitates hardware acceleration. Most approaches assume that the network architecture and parameters are unknown at design time, permitting usage…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…