Related papers: GeoLogic -- Graphical interactive theorem prover f…
Existing Graphical User Interface (GUI) reasoning tasks remain challenging, particularly in UI understanding. Current methods typically rely on direct screen-based decision-making, which lacks interpretability and overlooks a comprehensive…
Geometry problem solving has garnered increasing attention due to its potential applications in intelligent education field. Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents…
Prototypical part networks offer interpretable alternatives to black-box deep learning models by learning visual prototypes for classification. This work provides a comprehensive analysis of prototype formulations, comparing point-based and…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…
The task of crafting procedural programs capable of generating structurally valid 3D shapes easily and intuitively remains an elusive goal in computer vision and graphics. Within the graphics community, generating procedural 3D models has…
We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…
LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
Non-isotropic geometries are of interest to low-dimensional topologists, physicists and cosmologists. However, they are challenging to comprehend and visualize. We present novel methods of computing real-time native geodesic rendering of…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…
The goal of Inductive Logic Programming (ILP) is to learn a program that explains a set of examples. Until recently, most research on ILP targeted learning Prolog programs. The ILASP system instead learns Answer Set Programs (ASP). Learning…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
Recent advancements in multimodal large language models have driven breakthroughs in visual question answering. Yet, a critical gap persists, `conceptualization'-the ability to recognize and reason about the same concept despite variations…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…