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92edcfa | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 | """Fixed orthogonal transforms for packed low-bit linear layers.
The randomized Hadamard transform is block diagonal over the input feature
dimension. Both stored weight rows and row-major activations use the same
forward transform ``v -> (v * D) H``. Consequently, for orthogonal ``R = H D``
``linear(x, W) == linear(transform(x), transform(W))``.
Only the transformed weight is ternary and stored. The activation transform
must remain part of the deployed operator; materializing the inverse transform
into the weight would destroy the ternary representation.
"""
from __future__ import annotations
import math
import torch
import torch.nn as nn
import torch.nn.functional as F
from .quantization import hard_codes_scales
def _power_of_two(value: int) -> bool:
return value > 0 and value & (value - 1) == 0
def normalized_hadamard(value: torch.Tensor) -> torch.Tensor:
"""Apply an orthonormal Walsh-Hadamard transform on the last dimension."""
features = int(value.shape[-1])
if not _power_of_two(features):
raise ValueError("Hadamard dimension must be a positive power of two")
result = value
width = 1
prefix = value.shape[:-1]
while width < features:
paired = result.reshape(*prefix, -1, 2, width)
left = paired[..., 0, :]
right = paired[..., 1, :]
result = torch.cat((left + right, left - right), dim=-1).reshape(
*prefix, features
)
width *= 2
return result / math.sqrt(features)
def rademacher_signs(
groups: int,
group_size: int,
*,
seed: int,
device: torch.device | str,
dtype: torch.dtype,
) -> torch.Tensor:
"""Generate device-independent deterministic Rademacher signs."""
if groups < 1:
raise ValueError("groups must be positive")
if not _power_of_two(group_size):
raise ValueError("group_size must be a positive power of two")
generator = torch.Generator(device="cpu")
generator.manual_seed(int(seed))
bits = torch.randint(
0,
2,
(groups, group_size),
generator=generator,
dtype=torch.int8,
device="cpu",
)
return bits.to(device=device, dtype=dtype).mul(2).sub(1)
def blockwise_randomized_hadamard(
value: torch.Tensor,
*,
group_size: int = 128,
seed: int = 109,
) -> torch.Tensor:
"""Map row vectors to the randomized-Hadamard basis.
The last dimension must be exactly divisible by ``group_size``. Padding is
deliberately rejected because padding before an orthogonal transform would
change the represented linear operator.
"""
features = int(value.shape[-1])
if features % group_size:
raise ValueError("input features must be divisible by group_size")
groups = features // group_size
grouped = value.reshape(*value.shape[:-1], groups, group_size)
signs = rademacher_signs(
groups,
group_size,
seed=seed,
device=value.device,
dtype=value.dtype,
)
return normalized_hadamard(grouped * signs).reshape_as(value)
def inverse_blockwise_randomized_hadamard(
value: torch.Tensor,
*,
group_size: int = 128,
seed: int = 109,
) -> torch.Tensor:
"""Map transformed weight rows back to the original dense basis."""
features = int(value.shape[-1])
if features % group_size:
raise ValueError("input features must be divisible by group_size")
groups = features // group_size
grouped = value.reshape(*value.shape[:-1], groups, group_size)
signs = rademacher_signs(
groups,
group_size,
seed=seed,
device=value.device,
dtype=value.dtype,
)
return (normalized_hadamard(grouped) * signs).reshape_as(value)
class FixedTernaryLinear(nn.Module):
"""Inference-only ternary linear with identity or randomized-Hadamard input."""
def __init__(
self,
codes: torch.Tensor,
scales: torch.Tensor,
*,
compute_dtype: torch.dtype,
transform: str = "identity",
transform_seed: int = 109,
bias: torch.Tensor | None = None,
):
super().__init__()
if codes.ndim != 3 or scales.shape != codes.shape[:2]:
raise ValueError("codes must be [out, groups, group_size]")
if not torch.all((codes >= -1) & (codes <= 1)):
raise ValueError("codes must be ternary")
if transform not in {"identity", "rht"}:
raise ValueError("transform must be 'identity' or 'rht'")
self.register_buffer("ternary_codes", codes.detach().to(torch.int8))
self.register_buffer("group_scales", scales.detach().float())
if bias is not None:
self.register_buffer("bias", bias.detach().clone())
else:
self.bias = None
self.compute_dtype = compute_dtype
self.transform = transform
self.transform_seed = int(transform_seed)
self.in_features = int(codes.shape[1] * codes.shape[2])
self.out_features = int(codes.shape[0])
self.group_size = int(codes.shape[2])
self.register_buffer(
"_evaluation_weight",
(
self.ternary_codes.float()
* self.group_scales.unsqueeze(-1)
)
.reshape(self.out_features, self.in_features)
.to(compute_dtype),
persistent=False,
)
@classmethod
@torch.no_grad()
def from_weight(
cls,
weight: torch.Tensor,
*,
group_size: int = 128,
transform: str = "identity",
transform_seed: int = 109,
bias: torch.Tensor | None = None,
) -> "FixedTernaryLinear":
if weight.ndim != 2:
raise ValueError("weight must be a matrix")
if weight.shape[1] % group_size:
raise ValueError("weight input features must be divisible by group_size")
transformed = weight.detach().float()
if transform == "rht":
transformed = blockwise_randomized_hadamard(
transformed, group_size=group_size, seed=transform_seed
)
elif transform != "identity":
raise ValueError("transform must be 'identity' or 'rht'")
flat_codes, scales = hard_codes_scales(transformed, group_size)
codes = flat_codes.reshape(weight.shape[0], -1, group_size)
return cls(
codes,
scales,
compute_dtype=weight.dtype,
transform=transform,
transform_seed=transform_seed,
bias=bias,
)
def transformed_weight(self) -> torch.Tensor:
return self._evaluation_weight
def effective_weight(self) -> torch.Tensor:
value = self.transformed_weight()
if self.transform == "rht":
value = inverse_blockwise_randomized_hadamard(
value,
group_size=self.group_size,
seed=self.transform_seed,
)
return value.to(self.compute_dtype)
def forward(self, value: torch.Tensor) -> torch.Tensor:
if self.transform == "rht":
value = blockwise_randomized_hadamard(
value,
group_size=self.group_size,
seed=self.transform_seed,
)
weight = self.transformed_weight().to(value.dtype)
bias = None if self.bias is None else self.bias.to(value.dtype)
return F.linear(value, weight, bias)
def code_histogram(self) -> dict[int, int]:
values, counts = torch.unique(self.ternary_codes.cpu(), return_counts=True)
result = {-1: 0, 0: 0, 1: 0}
result.update(
{int(value): int(count) for value, count in zip(values, counts)}
)
return result
class TransformedProxyTernaryLinear(nn.Module):
"""Training wrapper for hard-forward proxy codes in a transformed basis.
``matrix.effective_weight()`` is expected to return the deployed weight in
transform space. The input transform stays explicit so no dense inverse
weight is materialized during forward.
"""
def __init__(
self,
matrix: nn.Module,
*,
transform: str = "rht",
transform_seed: int = 109,
bias: torch.Tensor | None = None,
):
super().__init__()
if transform not in {"identity", "rht"}:
raise ValueError("transform must be 'identity' or 'rht'")
if not hasattr(matrix, "effective_weight"):
raise TypeError("matrix must provide effective_weight()")
self.matrix = matrix
if bias is not None:
self.register_buffer("bias", bias.detach().clone())
else:
self.bias = None
self.transform = transform
self.transform_seed = int(transform_seed)
self.in_features = int(matrix.in_features)
self.out_features = int(matrix.out_features)
self.group_size = int(matrix.group_size)
def forward(self, value: torch.Tensor) -> torch.Tensor:
if self.transform == "rht":
value = blockwise_randomized_hadamard(
value,
group_size=self.group_size,
seed=self.transform_seed,
)
weight = self.matrix.effective_weight().to(value.dtype)
bias = None if self.bias is None else self.bias.to(value.dtype)
return F.linear(value, weight, bias)
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