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| """ | |
| Finite Scalar Quantization: VQ-VAE Made Simple - https://arxiv.org/abs/2309.15505 | |
| Code adapted from Jax version in Appendix A.1 | |
| """ | |
| from typing import List, Optional | |
| import torch | |
| import torch.nn as nn | |
| from torch.nn import Module | |
| from torch import Tensor, int32 | |
| from torch.cuda.amp import autocast | |
| from einops import rearrange, pack, unpack | |
| # helper functions | |
| def exists(v): | |
| return v is not None | |
| def default(*args): | |
| for arg in args: | |
| if exists(arg): | |
| return arg | |
| return None | |
| def pack_one(t, pattern): | |
| return pack([t], pattern) | |
| def unpack_one(t, ps, pattern): | |
| return unpack(t, ps, pattern)[0] | |
| # tensor helpers | |
| def round_ste(z: Tensor) -> Tensor: | |
| """Round with straight through gradients.""" | |
| zhat = z.round() | |
| return z + (zhat - z).detach() | |
| # main class | |
| class FSQ(Module): | |
| def __init__( | |
| self, | |
| levels: List[int], | |
| dim: Optional[int] = None, | |
| num_codebooks=1, | |
| keep_num_codebooks_dim: Optional[bool] = None, | |
| scale: Optional[float] = None, | |
| ): | |
| super().__init__() | |
| _levels = torch.tensor(levels, dtype=int32) | |
| self.register_buffer("_levels", _levels, persistent=False) | |
| _basis = torch.cumprod(torch.tensor([1] + levels[:-1]), dim=0, dtype=int32) | |
| self.register_buffer("_basis", _basis, persistent=False) | |
| self.scale = scale | |
| codebook_dim = len(levels) | |
| self.codebook_dim = codebook_dim | |
| effective_codebook_dim = codebook_dim * num_codebooks | |
| self.num_codebooks = num_codebooks | |
| self.effective_codebook_dim = effective_codebook_dim | |
| keep_num_codebooks_dim = default(keep_num_codebooks_dim, num_codebooks > 1) | |
| assert not (num_codebooks > 1 and not keep_num_codebooks_dim) | |
| self.keep_num_codebooks_dim = keep_num_codebooks_dim | |
| self.dim = default(dim, len(_levels) * num_codebooks) | |
| has_projections = self.dim != effective_codebook_dim | |
| self.project_in = nn.Linear(self.dim, effective_codebook_dim) if has_projections else nn.Identity() | |
| self.project_out = nn.Linear(effective_codebook_dim, self.dim) if has_projections else nn.Identity() | |
| self.has_projections = has_projections | |
| self.codebook_size = self._levels.prod().item() | |
| implicit_codebook = self.indices_to_codes(torch.arange(self.codebook_size), project_out=False) | |
| self.register_buffer("implicit_codebook", implicit_codebook, persistent=False) | |
| def bound(self, z: Tensor, eps: float = 1e-3) -> Tensor: | |
| """Bound `z`, an array of shape (..., d).""" | |
| half_l = (self._levels - 1) * (1 + eps) / 2 | |
| offset = torch.where(self._levels % 2 == 0, 0.5, 0.0) | |
| shift = (offset / half_l).atanh() | |
| return (z + shift).tanh() * half_l - offset | |
| def quantize(self, z: Tensor) -> Tensor: | |
| """Quantizes z, returns quantized zhat, same shape as z.""" | |
| quantized = round_ste(self.bound(z)) | |
| half_width = self._levels // 2 # Renormalize to [-1, 1]. | |
| return quantized / half_width | |
| def _scale_and_shift(self, zhat_normalized: Tensor) -> Tensor: | |
| half_width = self._levels // 2 | |
| return (zhat_normalized * half_width) + half_width | |
| def _scale_and_shift_inverse(self, zhat: Tensor) -> Tensor: | |
| half_width = self._levels // 2 | |
| return (zhat - half_width) / half_width | |
| def codes_to_indices(self, zhat: Tensor) -> Tensor: | |
| """Converts a `code` to an index in the codebook.""" | |
| assert zhat.shape[-1] == self.codebook_dim | |
| zhat = self._scale_and_shift(zhat) | |
| return (zhat * self._basis).sum(dim=-1).to(int32) | |
| def indices_to_codes(self, indices: Tensor, project_out=True) -> Tensor: | |
| """Inverse of `codes_to_indices`.""" | |
| is_img_or_video = indices.ndim >= (3 + int(self.keep_num_codebooks_dim)) | |
| indices = rearrange(indices, "... -> ... 1") | |
| codes_non_centered = (indices // self._basis) % self._levels | |
| codes = self._scale_and_shift_inverse(codes_non_centered) | |
| if self.keep_num_codebooks_dim: | |
| codes = rearrange(codes, "... c d -> ... (c d)") | |
| if project_out: | |
| codes = self.project_out(codes) | |
| if is_img_or_video: | |
| codes = rearrange(codes, "b ... d -> b d ...") | |
| return codes | |
| def forward(self, z: Tensor) -> Tensor: | |
| """ | |
| einstein notation | |
| b - batch | |
| n - sequence (or flattened spatial dimensions) | |
| d - feature dimension | |
| c - number of codebook dim | |
| """ | |
| is_img_or_video = z.ndim >= 4 | |
| # standardize image or video into (batch, seq, dimension) | |
| if is_img_or_video: | |
| z = rearrange(z, "b d ... -> b ... d") | |
| z, ps = pack_one(z, "b * d") | |
| assert z.shape[-1] == self.dim, f"expected dimension of {self.dim} but found dimension of {z.shape[-1]}" | |
| z = self.project_in(z) | |
| z = rearrange(z, "b n (c d) -> b n c d", c=self.num_codebooks) | |
| codes = self.quantize(z) | |
| indices = self.codes_to_indices(codes) | |
| codes = rearrange(codes, "b n c d -> b n (c d)") | |
| out = self.project_out(codes) | |
| # reconstitute image or video dimensions | |
| if is_img_or_video: | |
| out = unpack_one(out, ps, "b * d") | |
| out = rearrange(out, "b ... d -> b d ...") | |
| indices = unpack_one(indices, ps, "b * c") | |
| if not self.keep_num_codebooks_dim: | |
| indices = rearrange(indices, "... 1 -> ...") | |
| return out, indices | |