about "dimensional of high-order representations"

[foralliance]

您好，读了您的paper和code，有些疑问想咨询下：

1节4段指出：

In our case,d is usually very high (e.g., 512 or 2048 in [35, 16]), which results in much higher dimensional representations [28, 38] and suffering from high computation and memory costs.   
To overcome this problem,  we adopt polynomial  kernel  approximation  based  high-order  methods  [4],  which  can  efficiently  generate  low-dimensional high-order representations.  To this end,  the kernel representation can be reformulated with1×1 convolution operation followed by element-wise product

有2个疑问：

1. 结合Table2和prototxt中的内容，发现最终1,2,3阶特征的维度对应为1024,2048,4096．难道这3个维度还不算高吗？？
2. 您说可以使用＂polynomial kernel approximation方法＂去降维，实际中，就是用＂1×1 convolution operation followed by element-wise product＂，在prototxt中，确实有这个操作．但感觉这个操作主要是生成了high-order representation，跟降维没什么关系吧．难道可以理解为：这个操作在保证生成high-order representation的同时，也起到了降维的效果？？

麻烦了！！