encoding.py

# --- bulit in ---
import math
# --- 3rd party ---
import numpy as np
import torch
from torch import nn
# --- my module ---

"""
The MIT License (MIT)
Copyright (c) 2022 Joe Hsiao (Ending2015a)

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
OR OTHER DEALINGS IN THE SOFTWARE.
"""

# --- constants ---
PRIMES = [1, 2654435761, 805459861, 3674653429, 2097192037, 1434869437, 2165219737]


class Frequency(nn.Module):
  def __init__(
    self,
    dim: int,
    n_levels: int = 10
  ):
    """Positional encoding from NeRF: https://www.matthewtancik.com/nerf
    [sin(x), cos(x), sin(4x), cos(4x), sin(8x), cos(8x),
      ..., sin(2^n*x), cos(2^n*x)]

    Args:
      dim (int): input dimensions
      n_levels (int, optional): number of frequencies. Defaults to 10.
    """
    super().__init__()
    self.n_levels = n_levels
    assert self.n_levels > 0
    freqs = 2. ** torch.linspace(0., n_levels-1, n_levels)
    self.register_buffer('freqs', freqs, persistent=False)
    # ---
    self.input_dim = dim
    self.output_dim = dim * n_levels * 2
  
  def forward(self, x: torch.Tensor):
    x = x.unsqueeze(dim=-1) # (..., dim, 1)
    x = x * self.freqs # (..., dim, L)
    x = torch.cat((torch.sin(x), torch.cos(x)), dim=-1) # (..., dim, L*2)
    return x.flatten(-2, -1) # (..., dim * L * 2)


@torch.no_grad()
def fast_hash(ind: torch.Tensor, primes: torch.Tensor, hashmap_size: int):
  """Hashing function from:
  https://github.com/NVlabs/tiny-cuda-nn/blob/master/include/tiny-cuda-nn/encodings/grid.h#L76-L92
  """
  d = ind.shape[-1]
  ind = (ind * primes[:d]) & 0xffffffff  # uint32
  for i in range(1, d):
    ind[..., 0] ^= ind[..., i]
  return ind[..., 0] % hashmap_size

class _HashGrid(nn.Module):
  def __init__(
    self,
    dim: int,
    n_features: int,
    hashmap_size: int,
    resolution: float
  ):
    super().__init__()
    self.dim = dim
    self.n_features = n_features
    self.hashmap_size = hashmap_size
    self.resolution = resolution

    # you can add more primes for supporting more dimensions
    assert self.dim <= len(PRIMES), \
      f"HashGrid only supports < {len(PRIMES)}-D inputs"

    # create look-up table
    self.embedding = nn.Embedding(hashmap_size, n_features)
    nn.init.uniform_(self.embedding.weight, a=-0.0001, b=0.0001)

    primes = torch.tensor(PRIMES, dtype=torch.int64)
    self.register_buffer('primes', primes, persistent=False)

    # create interpolation binary mask
    n_neigs = 1 << self.dim
    neigs = np.arange(n_neigs, dtype=np.int64).reshape((-1, 1))
    dims = np.arange(self.dim, dtype=np.int64).reshape((1, -1))
    bin_mask = torch.tensor(neigs & (1 << dims) == 0, dtype=bool) # (neig, dim)
    self.register_buffer('bin_mask', bin_mask, persistent=False)

  def forward(self, x: torch.Tensor):
    # x: (b..., dim), torch.float32, range: [0, 1]
    bdims = len(x.shape[:-1])
    x = x * self.resolution
    xi = x.long()
    xf = x - xi.float().detach()
    xi = xi.unsqueeze(dim=-2) # (b..., 1, dim)
    xf = xf.unsqueeze(dim=-2) # (b..., 1, dim)
    # to match the input batch shape
    bin_mask = self.bin_mask.reshape((1,)*bdims + self.bin_mask.shape) # (1..., neig, dim)
    # get neighbors' indices and weights on each dim
    inds = torch.where(bin_mask, xi, xi+1) # (b..., neig, dim)
    ws = torch.where(bin_mask, 1-xf, xf) # (b...., neig, dim)
    # aggregate nehgibors' interp weights
    w = ws.prod(dim=-1, keepdim=True) # (b..., neig, 1)
    # hash neighbors' id and look up table
    hash_ids = fast_hash(inds, self.primes, self.hashmap_size) # (b..., neig)
    neig_data = self.embedding(hash_ids) # (b..., neig, feat)
    return torch.sum(neig_data * w, dim=-2) # (b..., feat)

class MultiResHashGrid(nn.Module):
  def __init__(
    self,
    dim: int,
    n_levels: int = 16,
    n_features_per_level: int = 2,
    log2_hashmap_size: int = 15,
    base_resolution: int = 16,
    finest_resolution: int = 512,
  ):
    """NVidia's hash grid encoding
    https://nvlabs.github.io/instant-ngp/

    The output dimensions is `n_levels` * `n_features_per_level`,
    or your can simply access `model.output_dim` to get the output dimensions

    Args:
      dim (int): input dimensions, supports at most 7D data.
      n_levels (int, optional): number of grid levels. Defaults to 16.
      n_features_per_level (int, optional): number of features per grid level.
        Defaults to 2.
      log2_hashmap_size (int, optional): maximum size of the hashmap of each
        level in log2 scale. According to the paper, this value can be set to
        14 ~ 24 depending on your problem size. Defaults to 15.
      base_resolution (int, optional): coarsest grid resolution. Defaults to 16.
      finest_resolution (int, optional): finest grid resolution. According to
        the paper, this value can be set to 512 ~ 524288. Defaults to 512.
    """
    super().__init__()
    self.dim = dim
    self.n_levels = n_levels
    self.n_features_per_level = n_features_per_level
    self.log2_hashmap_size = log2_hashmap_size
    self.base_resolution = base_resolution
    self.finest_resolution = finest_resolution

    # from paper eq (3)
    b = math.exp((math.log(finest_resolution) - math.log(base_resolution))/(n_levels-1))

    levels = []
    for level_idx in range(n_levels):
      resolution = math.floor(base_resolution * (b ** level_idx))
      hashmap_size = min(resolution ** dim, 2 ** log2_hashmap_size)
      levels.append(_HashGrid(
        dim = dim,
        n_features = n_features_per_level,
        hashmap_size = hashmap_size,
        resolution = resolution
      ))
    self.levels = nn.ModuleList(levels)

    self.input_dim = dim
    self.output_dim = n_levels * n_features_per_level

  def forward(self, x: torch.Tensor):
    return torch.cat([level(x) for level in self.levels], dim=-1)