My question

[DimanChauncey]

I want to know whether the ‘shape’ and the ‘rank’ in the tucker decomposition are always the same. Could their value be different？How are their value determined？
I'm a beginner in this area. Hope to reply to me.

[JeanKossaifi]

Hi @DimanChuancey sorry about the delay.
Rank is the rank of the decomposition so you can set it as you like.
In general lower than the shape (low-rank weighths), you could have a rank higher than the shape (over-parametrized). You can have a look at the doc. If you want a good intro to tensor decomposition I highly recommend the great survey by Kolda and Bader, “Tensor Decompositions and Applications”, SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.

[DimanChauncey]

Hi @DimanChuancey sorry about the delay.
Rank is the rank of the decomposition so you can set it as you like.
In general lower than the shape (low-rank weighths), you could have a rank higher than the shape (over-parametrized). You can have a look at the doc. If you want a good intro to tensor decomposition I highly recommend the great survey by Kolda and Bader, “Tensor Decompositions and Applications”, SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009.

Thanks! Good wishes!