Thread by @ankurhandos

I have been playing with my 2D toy example of NeRF (matthewtancik.com/nerf) that implemented to understand the role of positional encoding (PE).

code: github.com/ankurhanda/ner…

left is the dataset image, middle is results with PE and right is without it. It really helps.

This is the summary of my experiment

This figure in the paper really intrigued me arxiv.org/abs/2003.08934 so I set up a very toy 2D example to understand this. The difference in the results is significant.

Here are the results on **cool cows** image. Left is the dataset image, middle is the result with positional encoding and right without it.

I also think this has some semblance to the famous paper from rahimi & recht where they use random fourier features

Paper: people.eecs.berkeley.edu/~brecht/papers…

Most of the synthetic images I used in this experiment come from POVRay Hall of Fame

Glasses: hof.povray.org/glasses.html

Cool Cows: povray.org/community/hof/…

house image hof.povray.org/dhouse39.html

This is with random fourier features with scale and random phase shift

people.eecs.berkeley.edu/~brecht/papers…

Trying various periodic functions with scales and phase shifts (cc @peteflorence). Both scale and phase shift are needed.

Left is PE, middle is random fourier features and right is sawtooth.

All these functions seem to perform better than raw (x, y). It was meant as a fun experiment and I was more interested in finding various general class of functions that perform better at this experiment.

These are results with **8 layers of MLPs** of 128 features each with ReLU and BatchNorm.

Left is dataset image, middle is PE and right is raw (x, y).