Related papers: Using Machine Learning to Improve Cylindrical Alge…
In this paper we introduce the notion of an Open Non-uniform Cylindrical Algebraic Decomposition (NuCAD), and present an efficient model-based algorithm for constructing an Open NuCAD from an input formula. A NuCAD is a generalization of…
Cylindrical Algebraic Decomposition (CAD) by projection and lifting requires many iterated univariate resultants. It has been observed that these often factor, but to date this has not been used to optimise implementations of CAD. We…
In the paper which inspired the SC-Square project, [E. Abraham, Building Bridges between Symbolic Computation and Satisfiability Checking, Proc. ISSAC '15, pp. 1-6, ACM, 2015] the author identified the use of sophisticated heuristics as a…
The current trends in next-generation exascale systems go towards integrating a wide range of specialized (co-)processors into traditional supercomputers. Due to the efficiency of heterogeneous systems in terms of Watts and FLOPS per…
When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs,…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
Large Language Models (LLMs) have demonstrated impressive capabilities in a wide range of code generation tasks. However, generating code for certain domains remains challenging. One such domain is Computer-Aided Design (CAD) program, where…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Rapidly applying the effects of detector response to physics objects (e.g. electrons, muons, showers of particles) is essential in high energy physics. Currently available tools for the transformation from truth-level physics objects to…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…
Machine unlearning is becoming essential for building trustworthy and compliant language models. Yet unlearning success varies considerably across individual samples: some are reliably erased, while others persist despite the same…
Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by…