Complex Random Variables Enhance TensorSketch Sketching Efficiency

A new arXiv paper (2608.10523) introduces a method to improve the TensorSketch algorithm for high-dimensional polynomial kernel sketching by using complex-valued random variables. TensorSketch, originally developed by Pham and Pagh (2013) and Kar and Karnick (2012), provides efficient sketching for polynomial kernels, with the dense JL-type projection approach costing O(pDd) and the sparse CountSketch extension running in O(p(nnz(x) + D log D)). However, both estimators suffer from variance that grows exponentially with polynomial degree p, scaling as 3^p/D. Recent work by Wacker et al. (2023) showed that complex-valued distributions reduce this dependence to 2^p/D for the dense approach, but their method does not extend to the sparse CountSketch variant. This new paper likely extends the complex-valued technique to the sparse setting, potentially offering faster algorithms for high-dimensional sparse inputs with reduced variance. The paper is available on arXiv under the identifier 2608.10523, with an announcement type of 'cross'. The authors are not explicitly named in the provided content, but the citation references include Pham, Pagh, Kar, Karnick, and Wacker. The work is relevant to the fields of machine learning and randomized algorithms, particularly for kernel methods in high-dimensional spaces.