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While algorithmic fairness is a thriving area of research, in practice, mitigating issues of bias often gets reduced to enforcing an arbitrarily chosen fairness metric, either by enforcing fairness constraints during the optimization step,…
The study consists of two parts. Objective of the first part is modern language constructions responsible for algorithmically insolvability of parallelizing problem. Second part contains several ways to modify the constructions to make the…
The well known snapshot primitive in concurrent programming allows for n-asynchronous processes to write values to an array of single-writer registers and, for each process, to take a snapshot of these registers. In this paper we provide a…
The rapid trend of deploying artificial intelligence (AI) and machine learning (ML) systems in socially consequential domains has raised growing concerns about their trustworthiness, including potential discriminatory behaviours. Research…
We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the…
We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as…
Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, $f:X \to Y$. Leveraging the algebraic concept of transport of structure, we propose a method to explicitly identify non-standard…
Distributed multi-writer atomic registers are at the heart of a large number of distributed algorithms. While enjoying the benefits of atomicity, researchers further explore fast implementations of atomic reigsters which are optimal in…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Runtime verification is the process of verifying critical behavioral properties in big complex systems, where formal verification is not possible due to state space explosion. There have been several attempts to design efficient algorithms…
Embeddings play a pivotal role across various disciplines, offering compact representations of complex data structures. Randomized methods like Johnson-Lindenstrauss (JL) provide state-of-the-art and essentially unimprovable theoretical…
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
As machine learning systems are increasingly used to make real world legal and financial decisions, it is of paramount importance that we develop algorithms to verify that these systems do not discriminate against minorities. We design a…
State-of-the-art machine learning algorithms demonstrate close to absolute performance in selected challenges. We provide arguments that the reason can be in low variability of the samples and high effectiveness in learning typical…
There is an increasing body of literature proposing new and efficient persistent versions of concurrent data structures ensuring that a consistent state can be recovered after a power failure or a crash. Their correctness is typically…
Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…
In the shared variable model of concurrency, guarded atomic actions restrict the possible interference between processes by regions of atomic execution. The guard specifies the condition for entering an atomic region. That is a convenient…
Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…
Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite…