In[]:=
conv=NetInitialize@ConvolutionLayer[3,{3},"Stride"->3,"Input"->{1,9}]​​(*o1=k11i1+k12i2+k13i3,​​o2=k21i4+k22i5+k23i6,​​o3=k31i7+k32i8+k33i9*)
Out[]=
ConvolutionLayer
Input
:
matrix(size: 1×9)
Output
:
matrix(size: 3×3)

In[]:=
out=conv[{{1,2,3,4,5,6,7,8,9}}]
Out[]=
{{-3.13572,-6.89918,-10.6626},{1.69865,6.71775,11.7369},{-0.286465,-1.75429,-3.22212}}
In[]:=
k=NetExtract[conv,"Weights"]//Normal
Out[]=
{{{-0.293488,-0.040762,-0.920237}},{{0.887153,1.54616,-0.760273}},{{-0.631947,0.082531,0.06014}}}
​
In[]:=
k[[1]].{1,2,3}
Out[]=
{-3.13572}
In[]:=
k[[2]].{4,5,6}
Out[]=
{6.71775}
In[]:=
k[[3]].{7,8,9}
Out[]=
{-3.22212}