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In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using…
When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier…
The Cylindrical Algebraic Decomposition (CAD) method is currently the only complete algorithm used in practice for solving real-algebraic problems. To ameliorate its doubly-exponential complexity, different exploration-guided adaptations…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…
Computer-aided diagnosis (CAD), a vibrant medical imaging research field, is expanding quickly. Because errors in medical diagnostic systems might lead to seriously misleading medical treatments, major efforts have been made in recent years…
Virtual Diagnostic (VD) is a deep learning tool that can be used to predict a diagnostic output. VDs are especially useful in systems where measuring the output is invasive, limited, costly or runs the risk of damaging the output. Given a…
The Cylindrical Algebraic Decomposition (CAD) algorithm is a comprehensive tool to perform quantifier elimination over real closed fields. CAD has doubly exponential running time, making it infeasible for practical purposes. We propose to…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
Cylindrical algebraic decomposition (CAD) is a core algorithm within Symbolic Computation, particularly for quantifier elimination over the reals and polynomial systems solving more generally. It is now finding increased application as a…
The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within…
Efficient characterization of quantum devices is a significant challenge critical for the development of large scale quantum computers. We consider an experimentally motivated situation, in which we have a decent estimate of the…
Traditional TCAD simulation has succeeded in predicting and optimizing the device performance; however, it still faces a massive challenge - a high computational cost. There have been many attempts to replace TCAD with deep learning, but it…
The deployment of machine learning classifiers in high-stakes domains requires well-calibrated confidence scores for model predictions. In this paper we introduce the notion of variable-based calibration to characterize calibration…
As algorithms increasingly inform and influence decisions made about individuals, it becomes increasingly important to address concerns that these algorithms might be discriminatory. The output of an algorithm can be discriminatory for many…
High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
Coronary Artery Disease (CAD) is one of the leading causes of death worldwide, and so it is very important to correctly diagnose patients with the disease. For medical diagnosis, machine learning is a useful tool, however features and…
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose…