I am currently studying this article (p. 53), which proposes a convolution in a special way.
This is the formula:
Here is their explanation:
As shown in Figure 4.2, all maps of input functions (suppose I am a whole), O_i (i = 1, ..., I) are mapped into a series of function maps (suppose J as a whole), Q_j (j = 1, ···, J) in the convolution layers based on a number of local filters (total 1 × J), w_ {ij} (i = 1, ..., I; j = 1, · · ·, J). The mapping can be represented as a well-known convolution operation in signal processing. Assuming that the input function maps are all one-dimensional, each unit of one object map in the convolution layer can be calculated as the equation \ ref {eq: equation} (equation above).
where o_ {i, m} is the mth unit of the ith array of input data characteristics O_i, q_ {j, m} is the mth unit of the jth mapping of functions Q_j of the convolution layer, w_ {i, j, n} - the nth element of the weight vector w_ {i, j} connecting the i-th display of signs of entry into the j-th display of functions of the convolution layer, and F is called the size of the filter which represents the number of input bands that each unit of the convolution level receives.
So far so good:
What I basically understood from this, I tried to illustrate in this image.
It seems to me that they do, actually process all data points up to F and across all function maps. Basically moving in both directions xy and calculating points from that.
Isn't this a 2d convolution on a 2d image of size (I x F) with a filter equal to the image size ?. Weight doesn't seem to matter at all here.?
So why am I asking about this here.
I’m trying to realize this, I’m not sure what they are doing, it’s really just a basic convolution in which a sliding window tape continues to feed new data or that they do not normal convolution, which means that I need a special layer design, who performs this operation? ...