Intrinsic Low-Tucker-Rank Theory and Unified Tensor CUR Decomposition for High-Dimensional Hyperinterpolation

What the math gives to ML

The paper's transferable asset is a tensor-native compression strategy: represent a large coefficient tensor using selected fibers, a small intersection core, and orthonormal Tucker factors rather than storing every entry. This can be applied to tensorized neural-network weights, especially large MLP or convolution kernels, where mode-wise ranks are much smaller than the ambient dimensions. The most practical adaptation is a post-training or progressive-training TCUR-to-Tucker compressor with greedy index selection based on reconstruction residuals, followed by fine-tuning. The expected benefit is reduced parameter memory and lower inference cost, but the method should be tested against standard Tucker and tensor-train baselines because low-rank compression is already established in ML.