CvxNet: Can an autoencoder reconstruct an image exactly?

Hi!
Thank you for your work!

In the paper I see that you show examples where 2D b/w images are used as the autoencoder input (Figure 3, page 4), so as the output you have object exactly reconstructed by the half-planes (lines in 2D space).

Tell me, please, whether such experiments were carried out? Does the network actually restore the shape exactly?

I am interested in this for the reason that I decided to conduct similar experiments for my own purposes (with 2d b/w images with oriented rectangles along the coordinate axes, one rectangle per image), but I can't train the network. For one image, the network is trained well (and work on this example well), but if I train it using multiple images, the predictions (even on the training sample) in most cases are very bad at restoring the shape of rectangles.
It seems like it should work.

Some parameters I use:
n_half_planes = 15 # with a margin, although the rectangle has only 4 sides
n_parts = 1 # one rectangle per image
dims = 2 # b/w images
lr = 1e-4
latent_size = 10
Also, I use more light backbone.

Start with the CvxNet autoencoder discussion and Figure 3 on page 4, then compare the reported single-image and multiple-image behavior using the listed parameters. Done would require determining whether exact reconstruction was demonstrated and clarifying why rectangle shapes are poorly restored across multiple training images.