File size: 7,772 Bytes
cf5d356 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 | """Finite Scalar Quantization from https://arxiv.org/abs/2309.15505."""
from __future__ import annotations
import torch
from einops import pack, rearrange, unpack
from torch import Tensor, int32, nn
# helper functions
def _pack_single(
tensor: Tensor,
pattern: str,
) -> tuple[Tensor, list[torch.Size]]:
return pack([tensor], pattern)
def _unpack_single(
tensor: Tensor,
packed_shape: list[torch.Size],
pattern: str,
) -> Tensor:
return unpack(tensor, packed_shape, pattern)[0]
# tensor helpers
def straight_through_round(inputs: Tensor) -> Tensor:
"""Round with straight through gradients."""
rounded = inputs.round()
return inputs + (rounded - inputs).detach()
# main class
class FiniteScalarQuantizer(nn.Module):
"""Quantize continuous features into a product of scalar codebooks."""
def __init__(
self,
levels: list[int] | tuple[int, ...],
input_dimension: int | None = None,
output_dimension: int | None = None,
num_codebooks: int = 1,
keep_codebook_dimension: bool | None = None,
scale: float | None = None,
jitter_spread: float = 0.0,
) -> None:
super().__init__()
if not levels or any(level < 2 for level in levels):
raise ValueError("levels must contain integers greater than one.")
if num_codebooks <= 0:
raise ValueError("num_codebooks must be positive.")
if jitter_spread < 0:
raise ValueError("jitter_spread must be non-negative.")
_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_dimension = len(levels)
self.codebook_dimension = codebook_dimension
self.jitter_spread = jitter_spread
effective_codebook_dimension = codebook_dimension * num_codebooks
self.num_codebooks = num_codebooks
self.effective_codebook_dimension = effective_codebook_dimension
if keep_codebook_dimension is None:
keep_codebook_dimension = num_codebooks > 1
if num_codebooks > 1 and not keep_codebook_dimension:
raise ValueError(
"keep_codebook_dimension must be true with multiple codebooks."
)
self.keep_codebook_dimension = keep_codebook_dimension
self.input_dimension = (
input_dimension
if input_dimension is not None
else len(_levels) * num_codebooks
)
if self.input_dimension <= 0:
raise ValueError("input_dimension must be positive.")
has_projections = (
self.input_dimension != effective_codebook_dimension
)
self.input_projection = (
nn.Linear(self.input_dimension, effective_codebook_dimension)
if has_projections
else nn.Identity()
)
if output_dimension is not None:
self.output_projection = nn.Linear(
effective_codebook_dimension, output_dimension
)
else:
self.output_projection = (
nn.Linear(
effective_codebook_dimension, self.input_dimension
)
if has_projections
else nn.Identity()
)
self.has_projections = has_projections
self.codebook_size = int(self._levels.prod().item())
implicit_codebook = self.indices_to_codes(
torch.arange(self.codebook_size),
apply_output_projection=False,
)
self.register_buffer("implicit_codebook", implicit_codebook, persistent=False)
def bound_inputs(self, inputs: Tensor, epsilon: float = 1e-3) -> Tensor:
"""Bound inputs with shape (..., dimension)."""
if self.training and self.jitter_spread:
inputs = inputs + torch.randn_like(inputs) * self.jitter_spread
half_width = (self._levels - 1) * (1 - epsilon) / 2
offset = torch.where(self._levels % 2 == 0, 0.5, 0.0)
shift = (offset / half_width).tan()
return (inputs + shift).tanh() * half_width - offset
def quantize(self, inputs: Tensor) -> Tensor:
"""Quantize inputs and return values with the same shape."""
quantized = straight_through_round(self.bound_inputs(inputs))
half_width = self._levels // 2 # Renormalize to [-1, 1].
return quantized / half_width
def _normalized_to_code_coordinates(self, normalized_codes: Tensor) -> Tensor:
half_width = self._levels // 2
return (normalized_codes * half_width) + half_width
def _code_coordinates_to_normalized(self, codes: Tensor) -> Tensor:
half_width = self._levels // 2
return (codes - half_width) / half_width
def codes_to_indices(self, normalized_codes: Tensor) -> Tensor:
"""Convert normalized scalar codes to integer codebook indices."""
if normalized_codes.shape[-1] != self.codebook_dimension:
raise ValueError(
f"Expected code dimension {self.codebook_dimension}, "
f"received {normalized_codes.shape[-1]}."
)
code_coordinates = self._normalized_to_code_coordinates(
normalized_codes
)
return (code_coordinates * self._basis).sum(dim=-1).to(int32)
def indices_to_codes(
self,
indices: Tensor,
apply_output_projection: bool = True,
) -> Tensor:
"""Inverse of `codes_to_indices`."""
has_spatial_dimensions = indices.ndim >= (
3 + int(self.keep_codebook_dimension)
)
indices = rearrange(indices, "... -> ... 1")
code_coordinates = (indices // self._basis) % self._levels
codes = self._code_coordinates_to_normalized(code_coordinates)
if self.keep_codebook_dimension:
codes = rearrange(codes, "... c d -> ... (c d)")
if apply_output_projection:
codes = self.output_projection(codes)
if has_spatial_dimensions:
codes = rearrange(codes, "b ... d -> b d ...")
return codes
def forward(self, inputs: Tensor) -> tuple[Tensor, Tensor]:
"""Return quantized outputs and their integer codebook indices."""
has_spatial_dimensions = inputs.ndim >= 4
# standardize image or video into (batch, seq, dimension)
if has_spatial_dimensions:
inputs = rearrange(inputs, "b d ... -> b ... d")
inputs, packed_shape = _pack_single(inputs, "b * d")
if inputs.shape[-1] != self.input_dimension:
raise ValueError(
f"Expected input dimension {self.input_dimension}, "
f"received {inputs.shape[-1]}."
)
projected_inputs = self.input_projection(inputs)
projected_inputs = rearrange(
projected_inputs,
"b n (c d) -> b n c d",
c=self.num_codebooks,
)
codes = self.quantize(projected_inputs)
indices = self.codes_to_indices(codes)
codes = rearrange(codes, "b n c d -> b n (c d)")
outputs = self.output_projection(codes)
# reconstitute image or video dimensions
if has_spatial_dimensions:
outputs = _unpack_single(outputs, packed_shape, "b * d")
outputs = rearrange(outputs, "b ... d -> b d ...")
indices = _unpack_single(indices, packed_shape, "b * c")
if not self.keep_codebook_dimension:
indices = rearrange(indices, "... 1 -> ...")
return outputs, indices
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