Background: DCN is PointWise crossover, and it has been proved in this paper that DCN is essentially a scalar multiplication of input vector X0, which cannot achieve the effect of feature crossover.
Q: How do we use vector for feature crossing
A: Following the idea of FM, A vector can be constructed for each feature and represented by vector dot product.
Q: But a vector becomes a scalar after dot multiplication. How about n-order eigencross?
A: The dot product can be viewed as 1. HadaMard dot product 2. Sum. After the vector completes the HadaMard product, the vector is still a vector, so we lag the sum operation, can’t we do the n-order feature crossing?
Q: But there’s a problem: suppose you have M vectors, you cross them and you get M(m-1)/2 vectors. M of M minus one over two vectors crossed by two, that’s too big a magnitude.
A: Then let’s set K group weights and sum the M(m-1)/2 vectors into K group vectors. Can’t we complete k-order feature cross?
