Training-compatible backward-pass integration for TileGS

Extend the TileGS tile-local depth-binned rasterization pipeline to training by implementing a backward pass that traverses Gaussian–tile entries in the same tile-bin-major, selectively repaired order as the forward pass, thereby respecting the ordering dependence of alpha-compositing gradients.

Background

The presented TileGS implementation is limited to forward rasterization. Training requires gradients through the rasterization process, and the paper notes that alpha-compositing gradients depend on the exact ordering of Gaussian–tile entries. Consequently, a training-capable system must coordinate the backward traversal with the forward pipeline’s tile-bin-major organization and repair decisions.

The authors explicitly defer this integration, leaving unresolved the implementation of a backward pass that is compatible with TileGS’s binned and repaired ordering.