I was looking for "NeRF" in here but reading the paper it seems like they don't use neural networks to represent anything.

They seem to just optimize the positions and shapes of gaussian primitives as well as the reflectance properties.

Certainly a lot more "explainable" than a NeRF.

That's right. They use a fully differentiable renderer, which allows them to optimize the properties of this set of 3D gaussians using back propagation / gradient descent.

But ultimately what they end up with is an explicit representation of the scene, so unlike NeRF there's no "inference" during rendering. In that sense it's somewhere between a traditional mesh representation and an implicit representation like NeRF or signed distance fields. That's what makes it fast too; they get to make use of the rasterization acceleration capabilities of GPUs , unlike NeRFs which need to be sampled many times along a ray to render a scene.