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# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
import math
from typing import Any, Optional, Tuple
import numpy as np
import torch
from torch import nn
class PositionEmbeddingSine(nn.Module):
"""
This is a more standard version of the position embedding, very similar to the one
used by the Attention is all you need paper, generalized to work on images.
"""
def __init__(
self,
num_pos_feats,
temperature: int = 10000,
normalize: bool = True,
scale: Optional[float] = None,
):
super().__init__()
assert num_pos_feats % 2 == 0, "Expecting even model width"
self.num_pos_feats = num_pos_feats // 2
self.temperature = temperature
self.normalize = normalize
if scale is not None and normalize is False:
raise ValueError("normalize should be True if scale is passed")
if scale is None:
scale = 2 * math.pi
self.scale = scale
self.cache = {}
def _encode_xy(self, x, y):
# The positions are expected to be normalized
assert len(x) == len(y) and x.ndim == y.ndim == 1
x_embed = x * self.scale
y_embed = y * self.scale
dim_t = torch.arange(self.num_pos_feats, dtype=torch.float32, device=x.device)
dim_t = self.temperature ** (2 * (dim_t // 2) / self.num_pos_feats)
pos_x = x_embed[:, None] / dim_t
pos_y = y_embed[:, None] / dim_t
pos_x = torch.stack(
(pos_x[:, 0::2].sin(), pos_x[:, 1::2].cos()), dim=2
).flatten(1)
pos_y = torch.stack(
(pos_y[:, 0::2].sin(), pos_y[:, 1::2].cos()), dim=2
).flatten(1)
return pos_x, pos_y
@torch.no_grad()
def encode_boxes(self, x, y, w, h):
pos_x, pos_y = self._encode_xy(x, y)
pos = torch.cat((pos_y, pos_x, h[:, None], w[:, None]), dim=1)
return pos
encode = encode_boxes # Backwards compatibility
@torch.no_grad()
def encode_points(self, x, y, labels):
(bx, nx), (by, ny), (bl, nl) = x.shape, y.shape, labels.shape
assert bx == by and nx == ny and bx == bl and nx == nl
pos_x, pos_y = self._encode_xy(x.flatten(), y.flatten())
pos_x, pos_y = pos_x.reshape(bx, nx, -1), pos_y.reshape(by, ny, -1)
pos = torch.cat((pos_y, pos_x, labels[:, :, None]), dim=2)
return pos
@torch.no_grad()
def forward(self, x: torch.Tensor):
cache_key = (x.shape[-2], x.shape[-1])
if cache_key in self.cache:
return self.cache[cache_key][None].repeat(x.shape[0], 1, 1, 1)
y_embed = (
torch.arange(1, x.shape[-2] + 1, dtype=torch.float32, device=x.device)
.view(1, -1, 1)
.repeat(x.shape[0], 1, x.shape[-1])
)
x_embed = (
torch.arange(1, x.shape[-1] + 1, dtype=torch.float32, device=x.device)
.view(1, 1, -1)
.repeat(x.shape[0], x.shape[-2], 1)
)
if self.normalize:
eps = 1e-6
y_embed = y_embed / (y_embed[:, -1:, :] + eps) * self.scale
x_embed = x_embed / (x_embed[:, :, -1:] + eps) * self.scale
dim_t = torch.arange(self.num_pos_feats, dtype=torch.float32, device=x.device)
dim_t = self.temperature ** (2 * (dim_t // 2) / self.num_pos_feats)
pos_x = x_embed[:, :, :, None] / dim_t
pos_y = y_embed[:, :, :, None] / dim_t
pos_x = torch.stack(
(pos_x[:, :, :, 0::2].sin(), pos_x[:, :, :, 1::2].cos()), dim=4
).flatten(3)
pos_y = torch.stack(
(pos_y[:, :, :, 0::2].sin(), pos_y[:, :, :, 1::2].cos()), dim=4
).flatten(3)
pos = torch.cat((pos_y, pos_x), dim=3).permute(0, 3, 1, 2)
self.cache[cache_key] = pos[0]
return pos
class PositionEmbeddingRandom(nn.Module):
"""
Positional encoding using random spatial frequencies.
"""
def __init__(self, num_pos_feats: int = 64, scale: Optional[float] = None) -> None:
super().__init__()
if scale is None or scale <= 0.0:
scale = 1.0
self.register_buffer(
"positional_encoding_gaussian_matrix",
scale * torch.randn((2, num_pos_feats)),
)
def _pe_encoding(self, coords: torch.Tensor) -> torch.Tensor:
"""Positionally encode points that are normalized to [0,1]."""
# assuming coords are in [0, 1]^2 square and have d_1 x ... x d_n x 2 shape
coords = 2 * coords - 1
coords = coords @ self.positional_encoding_gaussian_matrix
coords = 2 * np.pi * coords
# outputs d_1 x ... x d_n x C shape
return torch.cat([torch.sin(coords), torch.cos(coords)], dim=-1)
def forward(self, size: Tuple[int, int]) -> torch.Tensor:
"""Generate positional encoding for a grid of the specified size."""
h, w = size
device: Any = self.positional_encoding_gaussian_matrix.device
grid = torch.ones((h, w), device=device, dtype=torch.float32)
y_embed = grid.cumsum(dim=0) - 0.5
x_embed = grid.cumsum(dim=1) - 0.5
y_embed = y_embed / h
x_embed = x_embed / w
pe = self._pe_encoding(torch.stack([x_embed, y_embed], dim=-1))
return pe.permute(2, 0, 1) # C x H x W
def forward_with_coords(
self, coords_input: torch.Tensor, image_size: Tuple[int, int]
) -> torch.Tensor:
"""Positionally encode points that are not normalized to [0,1]."""
coords = coords_input.clone()
coords[:, :, 0] = coords[:, :, 0] / image_size[1]
coords[:, :, 1] = coords[:, :, 1] / image_size[0]
return self._pe_encoding(coords.to(torch.float)) # B x N x C
# Rotary Positional Encoding, adapted from:
# 1. https://github.com/meta-llama/codellama/blob/main/llama/model.py
# 2. https://github.com/naver-ai/rope-vit
# 3. https://github.com/lucidrains/rotary-embedding-torch
def init_t_xy(end_x: int, end_y: int):
t = torch.arange(end_x * end_y, dtype=torch.float32)
t_x = (t % end_x).float()
t_y = torch.div(t, end_x, rounding_mode="floor").float()
return t_x, t_y
def compute_axial_cis(dim: int, end_x: int, end_y: int, theta: float = 10000.0):
freqs_x = 1.0 / (theta ** (torch.arange(0, dim, 4)[: (dim // 4)].float() / dim))
freqs_y = 1.0 / (theta ** (torch.arange(0, dim, 4)[: (dim // 4)].float() / dim))
t_x, t_y = init_t_xy(end_x, end_y)
freqs_x = torch.outer(t_x, freqs_x)
freqs_y = torch.outer(t_y, freqs_y)
freqs_cis_x = torch.polar(torch.ones_like(freqs_x), freqs_x)
freqs_cis_y = torch.polar(torch.ones_like(freqs_y), freqs_y)
return torch.cat([freqs_cis_x, freqs_cis_y], dim=-1)
def reshape_for_broadcast(freqs_cis: torch.Tensor, x: torch.Tensor):
ndim = x.ndim
assert 0 <= 1 < ndim
assert freqs_cis.shape == (x.shape[-2], x.shape[-1])
shape = [d if i >= ndim - 2 else 1 for i, d in enumerate(x.shape)]
return freqs_cis.view(*shape)
def apply_rotary_enc(
xq: torch.Tensor,
xk: torch.Tensor,
freqs_cis: torch.Tensor,
repeat_freqs_k: bool = False,
):
xq_ = torch.view_as_complex(xq.float().reshape(*xq.shape[:-1], -1, 2))
xk_ = (
torch.view_as_complex(xk.float().reshape(*xk.shape[:-1], -1, 2))
if xk.shape[-2] != 0
else None
)
freqs_cis = reshape_for_broadcast(freqs_cis, xq_)
xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(3)
if xk_ is None:
# no keys to rotate, due to dropout
return xq_out.type_as(xq).to(xq.device), xk
# repeat freqs along seq_len dim to match k seq_len
if repeat_freqs_k:
r = xk_.shape[-2] // xq_.shape[-2]
freqs_cis = freqs_cis.repeat(*([1] * (freqs_cis.ndim - 2)), r, 1)
xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(3)
return xq_out.type_as(xq).to(xq.device), xk_out.type_as(xk).to(xk.device)
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