In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Google's second generation of its AI mathematics system combines a language model with a symbolic engine to solve complex geometry problems better than International Mathematical Olympiad (IMO) gold ...

A comprehensive framework that combines quantum computing with geometric deep learning to achieve superior performance on both quantum and classical hardware. Based on geometric quantum computation ...

Abstract: In this paper, a new geometric snake model is proposed, based upon techniques of curve evolution and the utilization of gradient information and region information simultaneously. This model ...

Conceptual overview of this work. (A) Animals have goals, which they must learn to achieve. In this case, consider revising a paper. (B) Some feedback signals (e.g., from reviewers or co-authors) will ...

Noticed a problem while taking a look at the examples in this repository. It's barely noticeable, but there is a mistake in the “Ordinal Data” example. In this example the line color gradient was ...

After Albert Einstein published his special theory of relativity in 1905, he spent the next decade trying to come up with a theory of gravity. But for years, he kept running up against a problem. He ...