This report documents the program of the second Toulouse Tensor Workshop which took place at the University of Toulouse on September 17-19, 2025, and summarizes the main points of discussion. This workshop follows the first Workshop (CECAM workshop on Tensor Contraction Library Standardization), which took place in Toulouse one year earlier, on May 24-25, 2024 and led to the formation of a tensor standardization working group, which has since specified a low-level standard interface for tensor operations available freely on GitHub. The 2025 workshop brought together developers of applications which rely extensively on tensor computations such as quantum many-body simulations in chemistry and physics (material science and electronic structure calculations), as well as developers and experts of tensor software who have the know-how to provide the technical support for such applications. The workshop enabled the community to provide feedback on the specified low-level interface and how it can be further refined. It also initiated a discussion on how the standardization efforts should be oriented in the near feature, in particular on what should be higher-level interfaces and how to tackle other requirements of the community such as tensor decompositions, symmetric tensors and structured sparsity support.

翻译：本报告记录了于2025年9月17日至19日在图卢兹大学举办的第二届图卢兹张量研讨会的议程，并总结了讨论要点。本次研讨会是继首届研讨会（CECAM张量收缩库标准化研讨会）之后举办的，首届研讨会于一年前的2024年5月24日至25日在图卢兹举行，并促成了一个张量标准化工作组的成立。该工作组此后制定了一个低层次标准接口用于张量运算，并已在GitHub上开源提供。2025年的研讨会汇集了广泛依赖张量计算的应用程序开发者（例如化学与物理领域的量子多体模拟，包括材料科学和电子结构计算），以及具备为这类应用提供技术支持专长的张量软件开发者与专家。研讨会使得社区能够对已制定的低层次接口及其进一步优化方向提供反馈。会议还启动了关于近期标准化工作应如何推进的讨论，特别是关于应设计何种高层次接口，以及如何应对社区的其他需求，例如张量分解、对称张量和结构化稀疏性支持。