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from typing import Literal, Tuple
import torch
import torch.nn as nn
import numpy as np
def rope_rotate_half(x: torch.Tensor) -> torch.Tensor:
# x: [..., D], split into halves and rotate
x1, x2 = x.chunk(2, dim=-1)
return torch.cat([-x2, x1], dim=-1)
def rope_apply(
x: torch.Tensor,
sin: torch.Tensor,
cos: torch.Tensor
) -> torch.Tensor:
# x, sin, cos: [..., D]
return (x * cos) + (rope_rotate_half(x) * sin)
class RotaryPositionEmbedding(nn.Module):
"""
3D Rotary Positional Embedding (RoPE) with no mixing across axes (axial),
and no learnable weights. Allows for shifting and scaling of the positional encodings
for improving performance on varying resolutions.
Mirrors DINOv3 style but for (H, W, D).
Requirements:
- head_dim % 6 == 0 (because 3 axes -> periods of size head_dim//6, then we tile to fill head_dim)
Two parametrizations:
* base
* min_period + max_period
"""
def __init__(
self,
embed_dim: int,
*,
num_heads: int,
base: float | None = 1000.0, # works for common 8^3=512 to 16^3=4096 tokens
min_period: float | None = None,
max_period: float | None = None,
normalize_coords: Literal["min", "max", "separate"] = "separate",
shift_coords: float | None = None,
jitter_coords: float | None = None,
rescale_coords: float | None = None,
dtype: torch.dtype | None = None,
device: torch.device | None = None,
):
super().__init__()
assert embed_dim % num_heads == 0, "embed_dim must be divisible by num_heads"
head_dim = embed_dim // num_heads
assert head_dim % 6 == 0, "For 3D RoPE, (embed_dim // num_heads) must be divisible by 6"
both_periods = (min_period is not None) and (max_period is not None)
if (base is None and not both_periods) or (base is not None and both_periods):
raise ValueError("Either `base` or `min_period`+`max_period` must be provided.")
self.base = base
self.min_period = min_period
self.max_period = max_period
self.head_dim = head_dim
self.normalize_coords = normalize_coords
self.shift_coords = shift_coords
self.jitter_coords = jitter_coords
self.rescale_coords = rescale_coords
# Keep dtype persistent so teacher can be initialized from student state_dict()
self.dtype = dtype
self.register_buffer(
"periods",
torch.empty(self.head_dim // 6, device=device, dtype=dtype),
persistent=True,
)
self._init_weights()
@torch.no_grad()
def _init_weights(self):
device = self.periods.device
dtype = self.dtype
if self.base is not None:
# powers from 0..(head_dim // 3 - 1), normalized to [0, 1) across head_dim // 3?
# for 3D we use // 6 per axis
periods = self.base ** (
2 * torch.arange(self.head_dim // 6, device=device, dtype=dtype) / (self.head_dim // 3)
)
else:
# geometric spacing between min_period and max_period
base = self.max_period / self.min_period
exponents = torch.linspace(0, 1, self.head_dim // 6, device=device, dtype=dtype)
periods = base ** exponents
periods = periods / base
periods = periods * self.max_period
self.periods.data = periods
def forward(self, *, H: int, W: int, D: int) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Returns:
sin, cos: [H * W * D, head_dim] (per-head)
"""
device = self.periods.device
dtype = self.dtype
dd = dict(device=device, dtype=dtype)
# Prepare coords in [0, 1] then map to [-1, +1]
if self.normalize_coords == "max":
max_dim = max(H, W, D)
coords_h = torch.arange(0.5, H, **dd) / max_dim
coords_w = torch.arange(0.5, W, **dd) / max_dim
coords_d = torch.arange(0.5, D, **dd) / max_dim
elif self.normalize_coords == "min":
min_dim = min(H, W, D)
coords_h = torch.arange(0.5, H, **dd) / min_dim
coords_w = torch.arange(0.5, W, **dd) / min_dim
coords_d = torch.arange(0.5, D, **dd) / min_dim
elif self.normalize_coords == "separate":
coords_h = torch.arange(0.5, H, **dd) / H
coords_w = torch.arange(0.5, W, **dd) / W
coords_d = torch.arange(0.5, D, **dd) / D
else:
raise ValueError(f"Unknown normalize_coords: {self.normalize_coords}")
coords = torch.stack(
torch.meshgrid(coords_h, coords_w, coords_d, indexing="ij"),
dim=-1
) # [H, W, D, 3]
coords = coords.flatten(0, 2) # [HWD, 3]
coords = 2.0 * coords - 1.0 # [-1, +1]
# Optional train-time augmentations on coords (DINOv3)
if self.training and self.shift_coords is not None:
shift_hwd = torch.empty(3, **dd).uniform_(-self.shift_coords, self.shift_coords)
coords = coords + shift_hwd[None, :]
if self.training and self.jitter_coords is not None:
jit_max = np.log(self.jitter_coords); jit_min = -jit_max
jitter = torch.empty(3, **dd).uniform_(jit_min, jit_max).exp()
coords = coords * jitter[None, :]
if self.training and self.rescale_coords is not None:
r_max = np.log(self.rescale_coords); r_min = -r_max
rescale = torch.empty(1, **dd).uniform_(r_min, r_max).exp()
coords = coords * rescale
# --- Build angles per axis, then concatenate across axes ---
# coords: [N, 3] ; periods: [head_dim // 6]
# angles: [N, 3, head_dim // 6] -> flatten(1, 2) -> [N, head_dim // 2] -> tile(2) -> [N, head_dim]
angles = 2 * math.pi * coords[:, :, None] / self.periods[None, None, :] # [N, 3, head_dim // 6]
angles = angles.flatten(1, 2) # [N, head_dim // 2]
angles = angles.tile(2) # [N, head_dim]
cos = torch.cos(angles)
sin = torch.sin(angles)
return sin, cos
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