Related papers: Solving with GeoGebra Discovery an Austrian Mathem…
The Adam optimization method has achieved remarkable success in addressing contemporary challenges in stochastic optimization. This method falls within the realm of adaptive sub-gradient techniques, yet the underlying geometric principles…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS)…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
We present a comprehensive demonstration of how automated reasoning can assist mathematical research, both in the discovery of conjectures and in their verification. Our focus is a discrete geometry problem: What is $\mu_{5}(n)$, the…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
The emergence of "big data" offers unprecedented opportunities for not only accelerating scientific advances but also enabling new modes of discovery. Scientific progress in many disciplines is increasingly enabled by our ability to examine…
We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…
Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
The performance of gradient-based optimization methods, such as standard gradient descent (GD), greatly depends on the choice of learning rate. However, it can require a non-trivial amount of user tuning effort to select an appropriate…
We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a "quantum student" is being taught by a "classical teacher." In other words, in our method, the…
Automated driving object detection has always been a challenging task in computer vision due to environmental uncertainties. These uncertainties include significant differences in object sizes and encountering the class unseen. It may…
The sciences of biological and artificial intelligence are ever more intertwined. Neural computational principles inspire new intelligent machines, which are in turn used to advance theoretical understanding of the brain. To promote further…
Precise estimation of global orientation and location is critical to ensure a compelling outdoor Augmented Reality (AR) experience. We address the problem of geo-pose estimation by cross-view matching of query ground images to a…
Capturing uncertainty in object detection is indispensable for safe autonomous driving. In recent years, deep learning has become the de-facto approach for object detection, and many probabilistic object detectors have been proposed.…
We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we…
We present our method for automatically marking Physics exams. The marking problem consists in assessing typed student answers for correctness with respect to a ground truth solution. This is a challenging problem that we seek to tackle…
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…