Potential mathematical error for calculating con_o.y's gradient in backward process

[yangjiheng]

First of all, thank you for this wonderful project and elegant implementation which is both educative and precise from all aspects! This is really one of the world changing project in the history of computer science.

It came across to me that the constant factor for con_o.y in backward process is not consistent with forward process mathematically. But I'm not that sure about this, so I want to point this out and try to clear my doubts. Please help check whether this makes sense.

In forward process:

float power = -0.5f * (con_o.x * d.x * d.x + con_o.z * d.y * d.y) - con_o.y * d.x * d.y;

Then in the backward process, dL_dconic2D.y is calculated with:

atomicAdd(&dL_dconic2D[global_id].y, -0.5f * gdx * d.y * dL_dG);

To be consistent to the forward process, the constant factor of the gradient for con_o.y should be -1.0f, but the current implementation used -0.5f. So I wonder whether this is a minor mistake.

In this case, it should be implemented as:

atomicAdd(&dL_dconic2D[global_id].y, -1.0f * gdx * d.y * dL_dG);

I ran some experiments with updated factor and it seems OK quality-wise (not much improvement, but also not dropping in PSNR). So if this is a mathematical error, fixing this should make it more precise. Although it's highly possible that my understanding is not correct. Hence this PR to reach out to you guys to check it out. It could totally be some kind of technique or calculation error on my side that I'm not aware of.

Thanks again for sharing this with the rest of the us!

[dtjun]

试着推了一下

[yangjiheng]

试着推了一下

Exactly, so it makes sense for x and z to be -0.5, but for y, it should be -1.0 right?

[dtjun]

试着推了一下

Exactly, so it makes sense for x and z to be -0.5, but for y, it should be -1.0 right?

I think so