Question about PRB algorithm

[saeedhd96]

Hello,

I had a question, if we use Automatic differentation on path intergarator or also prb integrator, should they generate the exact same gradients?

In other words, is the following statement correct?
The only difference between these two integrators is the time and memory requirements and otherwise an optimization process using these two methods should look the exact same, given the same seed.

I get different results for optimizing materials in a room using these two integrators and I wonder why.

Thanks,
-Saeed

[njroussel]

Hi @saeedhd96

I believe you are correct. The path and prb integrators should produce the exact same primal image (noise included), and their gradients should match too.

You can maybe check the gradients at a single iteration to verify this.

[njroussel]

I can confirm this is at least the expected behaviour. In section 4.1 of Vicini et al. 2021:

Our method produces the same
result as automatic differentiation, while using a constant amount
of storage and retaining the linear time complexity of regular for-
ward path tracing. The results do not just match conventional AD in
expectation: they produce the same noise pattern, with only small
numerical differences related to the different evaluation in terms of
IEEE-754 floating point arithmetic.

The implementation might have a bug if this isn't true in practice 😞

[dvicini]

@saeedhd96 Hm yes it's possible that for some reason the seeding of these two integrators isn't consistent. But generally the statement is indeed true. Are you evaluating texture gradients?

[saeedhd96]

Please see this jupyter notebook, I am showing it on a scalar roughness parameter:

https://drive.google.com/drive/folders/16-wUN6of_MgakqUWW0mefwuWZYhFNJgZ?usp=sharing

[dvicini]

I see. Forward-mode is also quite different from reverse-mode for these integrators. So its possible that somewhere in there there is a difference in how the random numbers are consumed in these integrators.