Is hash necessary for proposed method?

[Jiang-Stan]

Hi, thanks for the great work! While reading the paper, I was impressed by using hash as an efficient storage-saving method. But I'm also curious if it's possible to implement storage multiplexing with remainders instead of hash tables, since hashing is not a very hardware friendly method, and remainders can regarded as a special hash result. So I tested the performance on some NeRF dataset after removing fast_hash implementation from the code, as is shown in this figure:

and I found that the performance is still impressive without using hash, as shown in following tables:

On NeRF_synthetic: data	steps=1000 w/ hash psnr	steps=1000 w/o hash psnr	steps=10000 w/ hash psnr	steps=10000 w/o hash psnr	steps=50000 w/ hash psnr	steps=50000 w/o hash psnr
lego	32.208	32.602	35.478	35.757	36.511	36.621
chair	31.476	31.255	34.129	33.490	34.994	34.385
drums	25.170	25.253	26.891	26.893	27.612	27.487
ficus	29.611	29.923	31.075	31.184	31.522	31.580
hotdog	34.856	34.827	37.524	37.246	38.328	37.957
materials	28.191	28.199	31.074	31.024	32.100	31.980
mic	32.968	32.730	36.180	35.701	37.214	36.759
ship	27.822	27.861	30.813	30.508	31.743	31.545

On Tartanair: data	w/ hash psnr	w/o hash psnr
abandonedfactory	17.278	17.438
amusement	20.346	20.398
carwelding	23.781	23.096
hospital	28.752	28.121
office2	26.315	26.531
seasonforest	19.134	18.172

I don't know if you have noticed this phenomenon before, because I didn't see hash related ablation experiments in the paper. Or is there anything I didn't noticed before in code that implemented hash?

If there is nothing wrong with code modification, is it possible to design a storage space representation to achieve a hardware-friendly mapping method that can achieve similar performance as hash did?

Thanks in advance for your reply!

[Tom94]

Hi there, thanks a lot for running these tests! You can actually use the TiledGrid mode of the encoding to obtain the "remainder" approach without any code changes.

We did experiment extensively with this, including hybrids, where the lower bits were tiled and the higher bits were hashed.

The key observations were:

• Tilings can give quite good PSNR, although usually worse than hashing and while exhibiting distinct visual artifacts that are less favorable than the "pseudorandom" distribution of the hash.
• These artifacts were often more visible in the neural radiance caching and SDF applications -- less so in NeRF specifically.
• Tiling doesn't actually improve hardware/cache locality and thus performance all that much. The actual computation of the hash value is effectively free -- only the memory access distribution matters. So since the hash uses 1 as the first "prime" number, your proposed modulo and the existing prime hash have very similar cache locality characteristics. The trade-off of these kinds of experiments never seemed favorable in the end.

[Tom94]

That said, you're 100% correct in that this discussion is missing from the paper. We really should add all this additional information for an updated version of it!

[Jiang-Stan]

Got it. Thanks a lot for your reply!

[ashawkey]

Hi, I wonder why TiledGrid mode limit each level's params by base_resolution instead of resolution here? This is different from simply commenting out the fash_hash part. Currently, TiledGrid mode uses much fewer parameters (total_encoding_params=131072) compared to HashGrid (total_encoding_params=12599920).

[Tom94]

In Tiled mode, it's good to be able to directly control the resolution of the tiled region, which is taken case of by base_resolution. If each level's parameters were controlled by resolution, then that'd be DenseGrid mode.

Also -- double-checking the code -- the tiling computation seems to be skewed at the moment due to a missing modulo by base_resolution in the inner loop of grid_index; my bad. I remember removing such a modulo operation due to it negatively affecting the dense & hash modes. Seems like I was overeager in trying to avoid code duplication.

[ashawkey]

Thanks for the explaining!