Optimal Evaluation of Symmetry-Adapted n-Correlations Via Recursive Contraction of Sparse Symmetric Tensors

02/08/2022

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by   Illia Kaliuzhnyi, et al.

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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.