calculation error when inverting a matrix

[ShuangtongLi]

Hi,
I am really interested in your model.I notice that your model requires every layer to be invertible.However,I did a simple test on calculation error when inverting a matrix.It can be viewd as a fully connected network.The result seems unacceptable(all elements in (a-copya) is between 10-100).My simple test code is as below.

import numpy as np
sizeb=1000
a=np.random.rand(1,sizeb)
copya=a
num=5
for i in range(num):
exec('weight'+str(i)+'=np.mat(np.random.rand(sizeb,sizeb))')
for i in range(num):
exec('a=np.dot(a,weight'+str(i)+')')
for i in range(num):
exec('a=np.dot(a,weight'+str(num-i-1)+'.I)')
print(a-copya)

I wonder why your model is able to be invertible,since even a shallow fully connected network get a large calculation error when inverting.I would really appreciate it if you could tell me why it is the case.Thanks a lot!