Phase IV — Vision: ViT, 3D, Video | Week 7 | 2.5 hours "Shifted windows: the trick that made vision transformers practical for dense prediction." — Liu et al., 2021
ViT computes global self-attention over all patches — $O(n^2)$ where $n$ is the number of patches. For a 224×224 image with 16×16 patches, $n = 196$. Manageable.
But for dense prediction tasks (object detection, segmentation) at higher resolutions: - 512×512, patch_size=4 → $n = 16{,}384$ patches → attention matrix is 16K × 16K - This is computationally infeasible
Swin Transformer computes attention within local windows, then shifts the windows to enable cross-window communication:
Stage 1: Window Attention Stage 2: Shifted Window Attention
┌───┬───┬───┬───┐ ┌──┬────┬────┬──┐
│ A │ A │ B │ B │ │ │ │ │ │
│ │ │ │ │ │──┼────┼────┼──│
│ A │ A │ B │ B │ shift by │ │ E │ F │ │
├───┼───┼───┼───┤ ──────────► │──┼────┼────┼──│
│ C │ C │ D │ D │ (M/2, M/2) │ │ G │ H │ │
│ │ │ │ │ │──┼────┼────┼──│
│ C │ C │ D │ D │ │ │ │ │ │
└───┴───┴───┴───┘ └──┴────┴────┴──┘
Attention in A,B,C,D: local Shifted: new windows E,F,G,H
cross previous boundaries!
For an image with $h \times w$ patches and window size $M$:
| Approach | Complexity |
|---|---|
| Global attention (ViT) | $O(h^2 w^2 \cdot d)$ — quadratic in image size |
| Window attention (Swin) | $O(h w \cdot M^2 \cdot d)$ — linear in image size |
With $M = 7$ (typical), attention is computed on $7 \times 7 = 49$ tokens per window — tiny and fixed!
Unlike ViT (single-scale), Swin produces multi-scale features like a CNN backbone:
Stage 1: 56×56, C=96 ← high resolution, fine features
│ Patch Merging (2×2 → 1, double channels)
▼
Stage 2: 28×28, C=192 ← medium resolution
│ Patch Merging
▼
Stage 3: 14×14, C=384 ← low resolution, semantic features
│ Patch Merging
▼
Stage 4: 7×7, C=768 ← coarsest features
Patch Merging: Concatenate 2×2 neighboring patches (4C channels) → linear projection to 2C.
This hierarchical design makes Swin a drop-in replacement for CNN backbones in detection (FPN) and segmentation (UPerNet).
Instead of absolute position embeddings, Swin uses relative position bias $B \in \mathbb{R}^{M^2 \times M^2}$:
$$\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d}} + B\right) V$$
This handles variable window positions and improves performance.
import torch
import torch.nn as nn
from einops import rearrange
def window_partition(x, window_size):
"""Partition feature map into non-overlapping windows.
Args:
x: (B, H, W, C)
window_size: int (M)
Returns:
windows: (B * num_windows, M, M, C)
"""
B, H, W, C = x.shape
x = x.view(B, H // window_size, window_size, W // window_size, window_size, C)
windows = x.permute(0, 1, 3, 2, 4, 5).contiguous()
windows = windows.view(-1, window_size, window_size, C)
return windows
def window_reverse(windows, window_size, H, W):
"""Reverse window_partition."""
B = int(windows.shape[0] / (H * W / window_size / window_size))
x = windows.view(B, H // window_size, W // window_size, window_size, window_size, -1)
x = x.permute(0, 1, 3, 2, 4, 5).contiguous().view(B, H, W, -1)
return x
class WindowAttention(nn.Module):
"""Window-based multi-head self-attention with relative position bias."""
def __init__(self, dim, window_size, n_heads):
super().__init__()
self.dim = dim
self.window_size = window_size
self.n_heads = n_heads
self.scale = (dim // n_heads) ** -0.5
self.qkv = nn.Linear(dim, 3 * dim)
self.proj = nn.Linear(dim, dim)
# Relative position bias table
# (2*M-1) * (2*M-1) possible relative positions
self.relative_position_bias_table = nn.Parameter(
torch.zeros((2 * window_size - 1) * (2 * window_size - 1), n_heads)
)
nn.init.trunc_normal_(self.relative_position_bias_table, std=0.02)
# Compute relative position index for each token pair
coords_h = torch.arange(window_size)
coords_w = torch.arange(window_size)
coords = torch.stack(torch.meshgrid(coords_h, coords_w, indexing='ij')) # (2, M, M)
coords_flat = coords.view(2, -1) # (2, M*M)
# Relative coordinates
relative_coords = coords_flat[:, :, None] - coords_flat[:, None, :] # (2, M*M, M*M)
relative_coords = relative_coords.permute(1, 2, 0).contiguous()
relative_coords[:, :, 0] += window_size - 1
relative_coords[:, :, 1] += window_size - 1
relative_coords[:, :, 0] *= 2 * window_size - 1
relative_position_index = relative_coords.sum(-1) # (M*M, M*M)
self.register_buffer("relative_position_index", relative_position_index)
def forward(self, x, mask=None):
B_, N, C = x.shape # B_ = batch * num_windows
head_dim = C // self.n_heads
qkv = self.qkv(x).reshape(B_, N, 3, self.n_heads, head_dim).permute(2, 0, 3, 1, 4)
q, k, v = qkv.unbind(0)
attn = (q @ k.transpose(-2, -1)) * self.scale
# Add relative position bias
bias = self.relative_position_bias_table[self.relative_position_index.view(-1)].view(
N, N, -1
).permute(2, 0, 1)
attn = attn + bias.unsqueeze(0)
if mask is not None:
attn = attn + mask.unsqueeze(1)
attn = attn.softmax(dim=-1)
out = (attn @ v).transpose(1, 2).reshape(B_, N, C)
return self.proj(out)
class SwinBlock(nn.Module):
"""Two consecutive Swin blocks: W-MSA then SW-MSA."""
def __init__(self, dim, n_heads, window_size=7, shift_size=0, mlp_ratio=4.0):
super().__init__()
self.window_size = window_size
self.shift_size = shift_size
self.norm1 = nn.LayerNorm(dim)
self.attn = WindowAttention(dim, window_size, n_heads)
self.norm2 = nn.LayerNorm(dim)
self.mlp = nn.Sequential(
nn.Linear(dim, int(dim * mlp_ratio)),
nn.GELU(),
nn.Linear(int(dim * mlp_ratio), dim),
)
def forward(self, x, H, W):
B, L, C = x.shape
x_reshaped = x.view(B, H, W, C)
# Cyclic shift
if self.shift_size > 0:
shifted = torch.roll(x_reshaped, shifts=(-self.shift_size, -self.shift_size), dims=(1, 2))
else:
shifted = x_reshaped
# Partition into windows
windows = window_partition(shifted, self.window_size)
windows = windows.view(-1, self.window_size * self.window_size, C)
# Window attention
attn_out = self.attn(self.norm1(windows).view(-1, self.window_size * self.window_size, C))
# Reverse windows
attn_out = attn_out.view(-1, self.window_size, self.window_size, C)
shifted = window_reverse(attn_out, self.window_size, H, W)
# Reverse cyclic shift
if self.shift_size > 0:
out = torch.roll(shifted, shifts=(self.shift_size, self.shift_size), dims=(1, 2))
else:
out = shifted
out = out.view(B, H * W, C)
x = x + out
x = x + self.mlp(self.norm2(x))
return x
Complexity comparison: For a 512×512 image with patch_size=4 and window_size=7, compute: - Number of patches (tokens) for ViT - Number of windows for Swin - FLOPs for global attention vs window attention
Shifted window visualization: Create a 8×8 grid and manually trace which tokens can attend to each other after one regular + one shifted window attention layer with window_size=4.
Use pretrained Swin: Load swin_tiny_patch4_window7_224 from timm and extract multi-scale features. Print the shapes at each stage.
Swin solved ViT's efficiency bottleneck. But both ViT and Swin need labeled data. Tomorrow: DINO learns visual features without any labels at all — through self-distillation.