import math
from typing import List, Tuple, Optional, Union
import torch
from torch import nn as nn
def pixel_freq_bands(
num_bands: int,
max_freq: float = 224.,
linear_bands: bool = True,
dtype: torch.dtype = torch.float32,
device: Optional[torch.device] = None,
):
if linear_bands:
bands = torch.linspace(1.0, max_freq / 2, num_bands, dtype=dtype, device=device)
else:
bands = 2 ** torch.linspace(0, math.log(max_freq, 2) - 1, num_bands, dtype=dtype, device=device)
return bands * torch.pi
def inv_freq_bands(
num_bands: int,
temperature: float = 100000.,
step: int = 2,
dtype: torch.dtype = torch.float32,
device: Optional[torch.device] = None,
) -> torch.Tensor:
inv_freq = 1. / (temperature ** (torch.arange(0, num_bands, step, dtype=dtype, device=device) / num_bands))
return inv_freq
def build_sincos2d_pos_embed(
feat_shape: List[int],
dim: int = 64,
temperature: float = 10000.,
reverse_coord: bool = False,
interleave_sin_cos: bool = False,
dtype: torch.dtype = torch.float32,
device: Optional[torch.device] = None
) -> torch.Tensor:
"""
Args:
feat_shape:
dim:
temperature:
reverse_coord: stack grid order W, H instead of H, W
interleave_sin_cos: sin, cos, sin, cos stack instead of sin, sin, cos, cos
dtype:
device:
Returns:
"""
assert dim % 4 == 0, 'Embed dimension must be divisible by 4 for sin-cos 2D position embedding'
pos_dim = dim // 4
bands = inv_freq_bands(pos_dim, temperature=temperature, step=1, dtype=dtype, device=device)
if reverse_coord:
feat_shape = feat_shape[::-1] # stack W, H instead of H, W
grid = torch.stack(
torch.meshgrid([torch.arange(s, device=device, dtype=dtype) for s in feat_shape])).flatten(1).transpose(0, 1)
pos2 = grid.unsqueeze(-1) * bands.unsqueeze(0)
# FIXME add support for unflattened spatial dim?
stack_dim = 2 if interleave_sin_cos else 1 # stack sin, cos, sin, cos instead of sin sin cos cos
pos_emb = torch.stack([torch.sin(pos2), torch.cos(pos2)], dim=stack_dim).flatten(1)
return pos_emb
def build_fourier_pos_embed(
feat_shape: List[int],
bands: Optional[torch.Tensor] = None,
num_bands: int = 64,
max_res: int = 224,
linear_bands: bool = False,
include_grid: bool = False,
concat_out: bool = True,
in_pixels: bool = True,
dtype: torch.dtype = torch.float32,
device: Optional[torch.device] = None,
) -> List[torch.Tensor]:
if bands is None:
if in_pixels:
bands = pixel_freq_bands(num_bands, float(max_res), linear_bands=linear_bands, dtype=dtype, device=device)
else:
bands = inv_freq_bands(num_bands, step=1, dtype=dtype, device=device)
else:
if device is None:
device = bands.device
if dtype is None:
dtype = bands.dtype
if in_pixels:
grid = torch.stack(torch.meshgrid(
[torch.linspace(-1., 1., steps=s, device=device, dtype=dtype) for s in feat_shape]), dim=-1)
else:
grid = torch.stack(torch.meshgrid(
[torch.arange(s, device=device, dtype=dtype) for s in feat_shape]), dim=-1)
grid = grid.unsqueeze(-1)
pos = grid * bands
pos_sin, pos_cos = pos.sin(), pos.cos()
out = (grid, pos_sin, pos_cos) if include_grid else (pos_sin, pos_cos)
# FIXME torchscript doesn't like multiple return types, probably need to always cat?
if concat_out:
out = torch.cat(out, dim=-1)
return out
class FourierEmbed(nn.Module):
def __init__(self, max_res: int = 224, num_bands: int = 64, concat_grid=True, keep_spatial=False):
super().__init__()
self.max_res = max_res
self.num_bands = num_bands
self.concat_grid = concat_grid
self.keep_spatial = keep_spatial
self.register_buffer('bands', pixel_freq_bands(max_res, num_bands), persistent=False)
def forward(self, x):
B, C = x.shape[:2]
feat_shape = x.shape[2:]
emb = build_fourier_pos_embed(
feat_shape,
self.bands,
include_grid=self.concat_grid,
dtype=x.dtype,
device=x.device)
emb = emb.transpose(-1, -2).flatten(len(feat_shape))
batch_expand = (B,) + (-1,) * (x.ndim - 1)
# FIXME support nD
if self.keep_spatial:
x = torch.cat([x, emb.unsqueeze(0).expand(batch_expand).permute(0, 3, 1, 2)], dim=1)
else:
x = torch.cat([x.permute(0, 2, 3, 1), emb.unsqueeze(0).expand(batch_expand)], dim=-1)
x = x.reshape(B, feat_shape.numel(), -1)
return x
def rot(x):
return torch.stack([-x[..., 1::2], x[..., ::2]], -1).reshape(x.shape)
def apply_rot_embed(x: torch.Tensor, sin_emb, cos_emb):
return x * cos_emb + rot(x) * sin_emb
def apply_rot_embed_list(x: List[torch.Tensor], sin_emb, cos_emb):
if isinstance(x, torch.Tensor):
x = [x]
return [t * cos_emb + rot(t) * sin_emb for t in x]
def apply_rot_embed_split(x: torch.Tensor, emb):
split = emb.shape[-1] // 2
return x * emb[:, :split] + rot(x) * emb[:, split:]
def build_rotary_pos_embed(
feat_shape: List[int],
bands: Optional[torch.Tensor] = None,
dim: int = 64,
max_freq: float = 224,
linear_bands: bool = False,
dtype: torch.dtype = torch.float32,
device: Optional[torch.device] = None,
):
"""
NOTE: shape arg should include spatial dim only
"""
feat_shape = torch.Size(feat_shape)
sin_emb, cos_emb = build_fourier_pos_embed(
feat_shape, bands=bands, num_bands=dim // 4, max_res=max_freq, linear_bands=linear_bands,
concat_out=False, device=device, dtype=dtype)
N = feat_shape.numel()
sin_emb = sin_emb.reshape(N, -1).repeat_interleave(2, -1)
cos_emb = cos_emb.reshape(N, -1).repeat_interleave(2, -1)
return sin_emb, cos_emb
class RotaryEmbedding(nn.Module):
""" Rotary position embedding
NOTE: This is my initial attempt at impl rotary embedding for spatial use, it has not
been well tested, and will likely change. It will be moved to its own file.
The following impl/resources were referenced for this impl:
* https://github.com/lucidrains/vit-pytorch/blob/6f3a5fcf0bca1c5ec33a35ef48d97213709df4ba/vit_pytorch/rvt.py
* https://blog.eleuther.ai/rotary-embeddings/
"""
def __init__(self, dim, max_res=224, linear_bands: bool = False):
super().__init__()
self.dim = dim
self.register_buffer('bands', pixel_freq_bands(dim // 4, max_res, linear_bands=linear_bands), persistent=False)
def get_embed(self, shape: List[int]):
return build_rotary_pos_embed(shape, self.bands)
def forward(self, x):
# assuming channel-first tensor where spatial dim are >= 2
sin_emb, cos_emb = self.get_embed(x.shape[2:])
return apply_rot_embed(x, sin_emb, cos_emb)