Regarding the number of grid parameters

[FDF521X]

Thank you for your excellent work. I have some questions. For multi-resolution hash grids, the number of parameters is primarily determined by the number of levels (n), feature dimension (dim), and hash size, where param = n 2^hash size dim. Therefore, a 2D hash grid and a 3D hash grid with the same resolution will have the same number of parameters, while three 2D hash grids will result in three times the number of parameters compared to a single hash grid of the same level. Is my understanding correct?

[lumennYan]

Great question! To my understanding, the number of parameters is determined by both the grid resolution and the hash size. At coarser levels of the hash grid, if I recall correctly, the encoding parameters don’t exceed the maximum hash size, leading to a smaller hash table. Assume the grid resolution is L, for three 2D hash grids, the number of parameters is 3*L^2, whereas for a 3D hash grid, it would be L^3. This means at lower levels of the hash grid, the 2D representation will have parameters an order of magnitude fewer than the 3D representation. However, when the number of parameters is greater than the hash table size, three 2D hash grids will result in three times the number of parameters compared to a single hash grid of the same level. I hope this helps clarify things!