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.
翻译:我们全面分析了用于评价在变换和旋转下变化不定的高维多元数值的算法。关键瓶颈是高维对称和稀疏的抗拉的收缩,其特定的聚度模式与多元体所强加的对称直接相关。我们提议明确构建循环评价战略,并表明在无限多元度限度内是最佳的。