Project DelphiTensors Workshop

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:

  1. Choose a CP rank.
  2. Count its stored parameters, R · sum(T.shape).
  3. Search Tucker ranks near that same parameter budget, and keep the one with the lowest reconstruction error.
  4. 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.