RI: Small: Reliable Machine Learning in Hyperbolic Spaces

许多人工智能（AI）方法通过将每个事物分配给空间中的一个点并使用几何处理它们来推理世界上的事物。这种人工智能推理单词的方式类似于在一张纸上写下许多单词，这样具有相似或相关含义的单词在页面上彼此靠近：这种地图被称为“嵌入”。“通常情况下，人工智能在将事物映射到曲面（例如球体的表面）而不是平面上时表现得更好。人类可能会发现这很难，因为需要在纸上的一个小空间中写入大量的单词;目前计算机上表示点的方式存在类似问题，限制了使用某些弯曲嵌入的AI的性能。这个项目将建立工具来缓解这个问题，让从业者使用弯曲嵌入，而不必担心他们的点如何在计算机上表示为比特。这将促进人工智能科学的进步，使这类强大的人工智能技术更容易为人类所用，并提高人工智能在处理自然语言和从社交网络学习等基本任务上的准确性。该项目将专注于“双曲空间”，这是一种具有恒定负曲率的齐次几何。双曲嵌入可以显着提高许多AI应用程序的性能，但使其对学习具有吸引力的相同属性也会为现有的机器学习框架带来严重的数值可靠性问题，这些框架是根据欧几里得几何设计的。该项目将通过构建一个新的双曲空间模型来解决这个问题，该模型可证明避免了现有方法的数值问题，同时仍然利用GPU的硬件加速功能来学习算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many artificial intelligence (AI) methods reason about things in the world by assigning each thing to a point in space and processing them using geometry. The way such an AI reasons about words is analogous to writing down many words on a piece of paper, such that words with similar or related meanings are located close to each other on the page: this map is called an "embedding." Often, AI perform better when they map things onto a curved surface (such as the surface of a sphere), rather than a flat one. A human might find this hard because of the need to write a large number of words into a small space on the paper; an analogous problem with the way points are represented on computers presently limits the performance of AI that use certain curved embeddings. This project will build tools to alleviate this problem, letting practitioners use curved embeddings without having to worry about how their points are represented as bits on a computer. This will promote the progress of AI science by making this powerful class of AI techniques more accessible to humans and improving the accuracy of AI on fundamental tasks such as processing natural language and learning from social networks.The project will focus on "hyperbolic space," which is a homogeneous geometry with constant negative curvature. Hyperbolic embeddings can significantly improve the performance of many AI applications, but the same properties that make it attractive for learning also create serious numerical reliability problems for existing machine learning frameworks, which were designed with Euclidean geometry in mind. This project will fix this by building a new model of hyperbolic space that provably avoids the numerical issues of existing approaches while still leveraging the hardware acceleration capabilities of GPUs for learning algorithms. Accomplishing this would improve the performance of learning in hyperbolic spaces and enable more people to train AIs using non-Euclidean space.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.