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import torch
def compute_bilinear_weights(grid):
"""
Compute bilinear weights for BilinearSoftmax
Args:
grid: [..., 2], (x, y)
Returns:
weights: [..., 4], [nw, ne, sw, se]
"""
x = grid[..., 0]
y = grid[..., 1]
x0 = torch.floor(x)
y0 = torch.floor(y)
dx = x - x0
dy = y - y0
nw = (1 - dx) * (1 - dy)
ne = dx * (1 - dy)
sw = (1 - dx) * dy
se = dx * dy
weights = torch.stack([nw, ne, sw, se], dim=-1)
return weights
def compute_match_attention(q, k, m_id, win_r, H, W):
"""
Args:
q: [B, N, h, C] # Query tensor
k: [B, N, h, C] # Key tensor
m_id: [B, N, h, 2] # Sampling centers, last dim is (x, y)
r: int # Sampling window radius
H: int # Height
W: int # Width
Returns:
output: [B, N, h, M] where M = (2*win_r[0]+2)*(2*win_r[1]+2)
"""
B, N, h, C = q.shape
M = (2*win_r[0] + 2)*(2*win_r[1] + 2)
dx = torch.arange(-win_r[0], win_r[0] + 2, device=q.device, dtype=torch.long)
dy = torch.arange(-win_r[1], win_r[1] + 2, device=q.device, dtype=torch.long)
dy, dx = torch.meshgrid(dy, dx, indexing='ij')
offsets = torch.stack((dx, dy), dim=-1).reshape(M, 2) # [M, 2]
centers = m_id.unsqueeze(3) # [B, N, h, 1, 2]
offsets = offsets.view(1, 1, 1, M, 2) # [1, 1, 1, M, 2]
coords = centers + offsets # [B, N, h, M, 2]
x_coords = coords[..., 0] # [B, N, h, M]
y_coords = coords[..., 1] # [B, N, h, M]
# Clamp coordinates to valid range
x_coords = x_coords.clamp(0, W-1)
y_coords = y_coords.clamp(0, H-1)
indices = y_coords * W + x_coords # [B, N, h, M]
# [B, N, h, C] -> [B, N, h, M, C]
k_expanded = k.unsqueeze(3).expand(-1, -1, -1, M, -1)
# [B, N, h, M] -> [B, N, h, M, C]
indices_gather = indices.unsqueeze(-1).expand(-1, -1, -1, -1, C)
# [B, N, h, M, C]
k_sampled = torch.gather(k_expanded, dim=1, index=indices_gather)
# [B, N, h, M, C] -> [B, N, h, M]
# negative L1 norm
output = -torch.abs(q.unsqueeze(3) - k_sampled).sum(dim=-1)
return output, indices_gather
def attn_scatter(attn, win_r):
"""
Scatter the attn to four sub-windows
Args:
attn: [B, N, h, M], M = (2*win_r[0]+2) * (2*win_r[1]+2)
win_r: window radius
Returns:
attn_sub: [B, N, h, 4, M_sub] attn for four sub-windows
"""
B, N, h, M = attn.shape
M_sub = (2*win_r[0] + 1)*(2*win_r[1] + 1)
# [B, N, h, H_win, W_win]
attn_2d = attn.view(B, N, h, 2*win_r[0] + 2, 2*win_r[1] + 2)
# nw [0, 0] offset
win_nw = attn_2d[..., :2*win_r[0]+1, :2*win_r[1]+1]
# ne [1, 0] offset
win_ne = attn_2d[..., :2*win_r[0]+1, 1:2*win_r[1]+2]
# sw [0, 1] offset
win_sw = attn_2d[..., 1:2*win_r[0]+2, :2*win_r[1]+1]
# se [1, 1] offset
win_se = attn_2d[..., 1:2*win_r[0]+2, 1:2*win_r[1]+2]
win_nw = win_nw.reshape(B, N, h, M_sub)
win_ne = win_ne.reshape(B, N, h, M_sub)
win_sw = win_sw.reshape(B, N, h, M_sub)
win_se = win_se.reshape(B, N, h, M_sub)
attn_sub = torch.stack([win_nw, win_ne, win_sw, win_se], dim=3)
return attn_sub
def attn_gather(attn_sub, win_r):
"""
Gather the four attn_sub to attn
Args:
attn_sub: [B, N, h, 4, M_sub]
win_r: window radius
Returns:
merged_attn: [B, N, h, M]
"""
B, N, h, _, M_sub = attn_sub.shape
merged = torch.zeros(B, N, h, 2*win_r[0] + 2, 2*win_r[1] + 2, device=attn_sub.device, dtype=attn_sub.dtype)
# nw [0, 0] offset
win_nw = attn_sub[:, :, :, 0, :].view(B, N, h, 2*win_r[0]+1, 2*win_r[1]+1)
merged[..., :2*win_r[0]+1, :2*win_r[1]+1] += win_nw
# ne [1, 0] offset
win_ne = attn_sub[:, :, :, 1, :].view(B, N, h, 2*win_r[0]+1, 2*win_r[1]+1)
merged[..., :2*win_r[0]+1, 1:2*win_r[1]+2] += win_ne
# sw [0, 1] offset
win_sw = attn_sub[:, :, :, 2, :].view(B, N, h, 2*win_r[0]+1, 2*win_r[1]+1)
merged[..., 1:2*win_r[0]+2, :2*win_r[1]+1] += win_sw
# se [1, 1] offset
win_se = attn_sub[:, :, :, 3, :].view(B, N, h, 2*win_r[0]+1, 2*win_r[1]+1)
merged[..., 1:2*win_r[0]+2, 1:2*win_r[1]+2] += win_se
merged_attn = merged.view(B, N, h, -1)
return merged_attn
def compute_bilinear_softmax(attn, bilinear_weight, win_r):
"""
Blinear Softmax: Attention sampled on a contiguous position
Args:
attn: [B, N, h, M] attention on discreate position
win_r: window radius
Returns:
output: [B, N, h, M] effective attention on contiguous position
"""
attn_sub = attn_scatter(attn, win_r) # [B, N, h, 4, M_sub]
attn_weighted = bilinear_weight.unsqueeze(-1)*attn_sub.softmax(dim=-1)
output = attn_gather(attn_weighted, win_r) # [B, N, h, M]
return output
def attention_aggregate(v, attn, indices_gather, win_r):
B, N, h, C = v.shape
M = (2*win_r[0] + 2)*(2*win_r[1] + 2)
# [B, N, h, C] -> [B, N, h, M, C]
v_expanded = v.unsqueeze(3).expand(-1, -1, -1, M, -1)
v_sampled = torch.gather(v_expanded, dim=1, index=indices_gather)
output = (attn.unsqueeze(-1)*v_sampled).sum(dim=3)
return output.view(B, N, -1)
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