Improving Tensor Decoupling with Scaling and Smoothing

This thesis presents two improvements to tensor decoupling algorithms, which are methods to decompose multivariate "black-box" functions into structured decoupled representations. First, a tensor scaling preprocessing step normalizes gradient magnitudes across all outputs, enabling robust decoupling of functions with highly mismatched gradient and output ranges. Second, splines coupled with a smoothing prior and generalized cross-validation are used to make the method non-parametric with respect to the number of control points. These contributions are combined into a unified new algorithm, validated on a neural network compression task, and released as Untangle, the first open-source Python library for tensor decoupling.