""" Sin-cos, fourier, rotary position embedding modules and functions Hacked together by / Copyright 2022 Ross Wightman """ 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)