How to understand downsampling

[Sinking-Stone]

Hello, I'm very sorry to bother you again. When I read your source code, I don't quite understand how your downsampling is calculated. Could you explain it to me, because it is just a simple description in your paper.

[narger-ef]

Essentially there are 3 phases, I take Ctxt FHEController::downsample1024to256(const Ctxt &c1, const Ctxt &c2) { as an example:

(notice the line numbers in the image)

This is needed because some slots will be empty, because the previous convolution has some blank values (because of the stride equal to 2)

[Sinking-Stone]

Can you explain line 346 what is in the main.cpp vector<Ctxt> res1sx = controller.convbn1632sx(boot_in, 4, 1, scaleSx, timing); //Questo e lento vector<Ctxt> res1dx = controller.convbn1632dx(boot_in, 4, 1, scaleDx, timing); //Questo e lento What does this do? I don't understand it from this place. Can you explain what sx and dx are? How can I understand them better?

[narger-ef]

I refer you to this, especially the image

[Sinking-Stone]

Oh, I have understood sx and dx, but I still can't connect the picture you gave me in the downsampling with the code. Could you give me an example? Thank you very much.

[narger-ef]

The fourth block (in figure) has two branches: sx and dx

both do a downsampling (on the sx immediately, on the dx after the first convolution)

[Sinking-Stone]

Yes, I already know this, what I don't understand is the line corresponding to the code in the figure below.

[narger-ef]

Ah ok. The "re-arranging" figure is the procedure performed inside the Conv2D blocks, since they have a stride of {2, 2}. This means that the kernel window is shifted by 2 positions (and not by 1, as in previous convolutions), leaving one block empty in our ciphertexts (because the HE convolution assumes that the stride is equal to {1, 1}). For this reason, we have to re-arrange the values in order to fill the empty slots

[Sinking-Stone]

Simulation of FHEController 1191-1194

def rot(nums,index):
    index=index%len(nums)
    if(index>0):
        return nums[index:]+nums[:index]
    else:
        return nums[-index:]+nums[:-index]

def create_vec(n):
    res=[]
    for i in range(1,n+1):
        line=[i]
        res.append(line)
    return res

def vec_add(vec1,vec2):
    for i in range(len(vec1)):
        if vec2[i]==[0]:
            continue
        elif vec1[i]==[0]:
            vec1[i]=vec2[i]
        else:
            vec1[i].extend(vec2[i])
    return vec1

def vec_mult(vec1,vec2):
    for i in range(len(vec1)):
        if vec2[i]==0:
            vec1[i]=[0]

    return vec1

def gen_mask(n):
    mask=[]
    ci=n
    for i in range(1,32*32*32+1):
        if ci>0 :
            mask.append(1)
        else:
            mask.append(0)
        ci-=1
        if ci<=-n:
            ci=n
    return mask

if __name__ == '__main__':

    with open('test.txt','w') as f:
        fullpacke=create_vec(32*32*32)
        fullpacke=vec_mult(vec_add(fullpacke,rot(fullpacke,1)),gen_mask(2))
        f.write(str(fullpacke))
        f.write('\n------------------------------------------------------------------------------------------\n')
        fullpacke=vec_mult(vec_add(fullpacke,rot(fullpacke,2)),gen_mask(4))
        f.write(str(fullpacke))
        f.write('\n------------------------------------------------------------------------------------------\n')
        fullpacke=vec_mult(vec_add(fullpacke,rot(fullpacke,4)),gen_mask(8))
        f.write(str(fullpacke))
        f.write('\n------------------------------------------------------------------------------------------\n')
        fullpacke=vec_add(fullpacke,rot(fullpacke,8))
        f.write(str(fullpacke))

I am very sorry that I have been simulating your program, the numbers in my code represent subscripts, maybe there is something wrong with my writing, I am different from the diagram you gave, could you give me an example about the subsampling code? Thank you very much.