论文标题
通过稀疏对称张量的递归收缩对对称适应的$ n $相关的最佳评估
Optimal Evaluation of Symmetry-Adapted $n$-Correlations Via Recursive Contraction of Sparse Symmetric Tensors
论文作者
论文摘要
我们提供了用于评估在排列和旋转下不变的高维多项式的算法的综合分析。关键的瓶颈是高维对称和稀疏张量的收缩，具有特定的稀疏模式，与施加在多项式上的对称性直接相关。我们提出了递归评估策略的明确结构，并表明它在无限多项式程度的极限上是最佳的。
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.
