张量学习与正交、洛伦兹和辛对称性
Tensor learning with orthogonal, Lorentz, and symplectic symmetries
AI总结：
本文提出了一种基于正交、洛伦兹和辛对称性的张量学习方法，通过等变架构提升时间序列、材料科学和理论计算机科学中的模型性能。
摘要：
张量是一种在许多科学领域中基本的数据结构，例如时间序列分析、材料科学和物理等领域。提高我们产生和处理张量的能力对于高效解决这些问题至关重要。在本文中，我们展示了如何利用将张量映射到张量的函数的内在对称性。更具体地说，我们开发了能够普遍表达的等变机器学习架构，这些架构利用了在许多情况下这些张量函数相对于正交、洛伦兹和/或辛群的对角作用是等变的这一事实。我们展示了在材料科学、理论计算机科学和时间序列分析中的三个问题上的结果。对于时间序列，我们将我们的方法与日益流行的路径签名方法结合，后者也对重新参数化具有不变性。我们的数值实验表明，我们的等变模型在相应非等变基线之上表现更好。
英文摘要：
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in many cases, these tensor functions are equivariant with respect to the diagonal action of the orthogonal, Lorentz, and/or symplectic groups. We showcase our results on three problems coming from material science, theoretical computer science, and time series analysis. For time series, we combine our method with the increasingly popular path signatures approach, which is also invariant with respect to reparameterizations. Our numerical experiments show that our equivariant models perform better than corresponding non-equivariant baselines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
