基于稀疏对称张量递归压缩的对称自适应$n$ -相关的最优估计
Optimal Evaluation of Symmetry-Adapted $n$-Correlations Via Recursive Contraction of Sparse Symmetric Tensors
摘要：
我们提出了一个全面的分析，用于评估高维多项式的排列和旋转下不变的算法。关键的瓶颈是一个高维的对称和稀疏张量的收缩与特定的稀疏模式，这是直接相关的对称性施加在多项式上。我们提出了一个显式构造的递归评估策略，并证明了它是最优的无限多项式次数的限制。
英文摘要：
We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant under permutations and rotations. The key bottleneck is the contraction of a high-dimensional symmetric and sparse tensor with a specific sparsity pattern that is directly related to the symmetries imposed on the polynomial. We propose an explicit construction of a recursive evaluation strategy and show that it is optimal in the limit of infinite polynomial degree.
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。
