Some questions about the code and equations in paper

[zhujiagang]

An excellent work! I've several questions.

1. Why does the par appear in out_grad, while par_pos in out_data?

   TreeFilter-Torch/furnace/kernels/lib_tree_filter/src/refine/refine.cu

   Line 184 in 4eed6b6

   float right = in_data[cur + data_offset] * (out_grad[par + grad_offset] - edge_weight * in_grad[cur + grad_offset]);

2. delta S(Ei,j)/delta wi,j in eq.9 seems to disappear in the code.

   TreeFilter-Torch/furnace/kernels/lib_tree_filter/src/refine/refine.cu

   Line 367 in 4eed6b6

   grad_weight_tensor = (grad_all_channel_tensor - grad_norm_all_channel_tensor).sum(1);

3. The paper says "uniformly sample a vertex as the root and perform breadth-first sorting (BFS) algorithm to obtain the topological order of tree G“. But it seems that the code always start from the index 0.
   

   TreeFilter-Torch/furnace/kernels/lib_tree_filter/src/bfs/bfs.cu

   Line 79 in 4eed6b6

   if ((sorted_index[i] > 0) || (i == 0)){

[StevenGrove]

Thanks for your interest in our work.

1. Because out_data is ordered as the input feature, but out_grad is ordered in the breadth-first-search (BFS) manner.
2. The "weight" in "refine.cu" is already calculated by S(Ei, j), whose gradient is obtained by using the native PyTorch code. Please refer to the distance_func

   TreeFilter-Torch/furnace/kernels/lib_tree_filter/modules/tree_filter.py

   Line 29 in 4eed6b6

   weight_row = self.distance_func(fm[:, :, :-1, :], fm[:, :, 1:, :])

3. In the BFS algorithm, different vertexes as the root, the algorithm will output a consistent topology. For convenience, we choose the first vertex as the root.

[zhujiagang]

Got It! Thank you very much!