What each core costs to store

• CP stores R·ΣIₙ numbers: linear in R.
• Tucker stores ΠRₙ + ΣIₙRₙ: the core’s product grows fastest. A mode kept whole (Rₙ = Iₙ) stores no factor.

def cp_numbers(shape, rank):
    return rank * sum(shape)

def tucker_numbers(shape, ranks):
    core = int(np.prod(ranks))
    factors = sum(n * r for n, r in zip(shape, ranks) if r < n)
    return core + factors

On a 256 × 256 × 3 × 3 convolution kernel at rank 100, CP stores 51,800 numbers (518R) and Tucker-2 at (100, 100, 3, 3) stores 141,200 (512R + 9R²), about 2.7× as many. 90,000 of them are core entries.

But equal rank is the wrong comparison: at equal rank Tucker fits at least as well. A count tells you the price of a model, not what it buys.