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W1. The authors have clearly reduced whitespace throughout the paper; equations are crammed together, captions are too close to the figures. This by itself is grounds for rejection since it effectively violates the 9-page paper limit.
W2. An important weakness that is not mentioned anywhere is that the factors A ( k )
in Eq (8) must have dimensions that factorize the dimensions of W
. For example, they must satisfy ∏ k = 1 S a j ( k ) = w j
. So what is hailed as greater flexibility of the proposed model in the caption of Fig 1 is in fact a limitation. For example, if the dimensions of W
are prime numbers, then for each mode of W
, only a single tensor A ( k )
can have a non-singleton dimension in that same mode. This may be fixable with appropriate zero padding, but this has to at least be discussed and highlighted in the paper.
W3. The 2nd point in the list of contributions in Sec 1 claims that the paper provides a means of finding the best approximation in the proposed format. In fact, it is easy to see that this claim is likely to be false: The decomposition corresponds to a difficult non-convex optimization problem, and it is therefore unlikely that a simple algorithm with a finite number of steps could solve it optimally.
W4. SeKron is claimed to generalize various other decompositions. But it is not clear that the proposed algorithm could ever reproduce those decompositions. For example, since there is no SVD-based algorithm for CP decomposition, I strongly suspect that the proposed algorithm (which is SVD-based) cannot recreate the decomposition that, say, an alternating least squares based approach for CP decomposition would achieve.
W5. The paper is unclear and poor notation is used in multiple places. For examples:
Subscripts are sometimes used to denote indices (e.g., Eq (5)), sometimes to denote sequences of tensors (e.g., Eqs (7), (8)), and sometimes used to denote both at the same time (e.g., Thm 3, Eq (35))! This is very confusing.
It is unclear how Eq (7) follows from Eq (5). The confusing indices exacerbate this.
In Thm 1, A ( k )
are tensors, so it's unclear what you mean by " R i
are ranks of intermediate matrices".
In Alg 1, you apply SVD to a 3-way tensors. This operation is not defined. If you mean batched SVD, you need to specify that. The W r 1 ⋯ r k − 1 ( k )
tensors in Eq (10) haven't been defined.
The definition of Unfold below Eq (13) is ambiguous. Similarly, you say that Mat reformulates a tensor to a matrix, but list the output space as R d 1 ⋯ d N
, i.e., indicating that the output is a vector.
Below Eq (15) you discuss "projection". This is not an appropriate term to use, since these aren't projections; projection is a term with a specific meaning in linear algebra.
In Eq (16), the r k
indices appear on the right-hand side but not on the left-hand side.
--- W1. The authors have clearly reduced whitespace throughout the paper; equations are crammed together, captions are too close to the figures. This by itself is grounds for rejection since it effectively violates the 9-page paper limit.