Compare at a matched parameter budget
Do not compare CP rank R against Tucker rank (R, R, R). Those two representations store different numbers of parameters, so the comparison measures the budget, not the model.
A fair experiment:
- Choose a CP rank.
- Count its stored parameters,
R · sum(T.shape). - Search Tucker ranks near that same parameter budget, and keep the one with the lowest reconstruction error.
- Compare error and interpretability at that matched budget.
Step 3 is where this goes wrong most easily. Picking the candidate whose parameter count is merely closest to the budget can hand Tucker a degenerate rank-1 mode, and manufacture the conclusion.