Using fourier feature mapping Strengthen GON (《Gradient Origin Networks》)'s performance

The origin GON could quickly learn a latent representation by introducing a second-order derivative and SIREN.

It get a good performance on MNIST, but not good for Celeba:

Recon for Celeba

As shown in the figure above, the recon is very blurry, and it's very easy to cause gradient explosion. Which can be considered that it cannot learn high-frequency functions.

As mentioned earlier, current models need a mechanism to learn high-frequency functions. Fortunately, recently proposed 《Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains》 Just do it.

Simply apply fourier mapping on coordinates, let's see the result:

Recon for Celeba after apply fourier

Wow! Considerable improvement!

The appearance of SIREN makes it possible to calculate the second derivative, so the emergence of GON is natural. It's a good way to learning image embedding, and could be used with Image retrieval, face recognition, and so on. But calculation speed and memory footprint are still an issue.