Tensor Power

Tensor power methods are iterative algorithms used to decompose high-dimensional tensors, a crucial task in various fields like machine learning and statistics. Current research focuses on improving the efficiency and robustness of these methods, particularly for higher-order tensors and in the presence of noise, exploring techniques like sketching and analyzing the convergence properties of power iteration under different initialization strategies and signal-to-noise ratios. These advancements are significant because efficient tensor decomposition enables improved performance in applications ranging from tensor PCA to the development of group-equivariant neural networks, which leverage tensor power spaces to incorporate symmetries into deep learning models.