File size: 5,972 Bytes
ad9fbbf | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 | import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from .self_attention import Normalize, gather_edges, gather_nodes
class PositionalEncodings(nn.Module):
def __init__(self, num_embeddings):
super(PositionalEncodings, self).__init__()
self.num_embeddings = num_embeddings
def forward(self, E_idx):
# i-j
N_batch = E_idx.size(0)
N_nodes = E_idx.size(1)
N_neighbors = E_idx.size(2)
device = E_idx.device
ii = torch.arange(N_nodes, dtype=torch.float32, device=device).view((1, -1, 1))
d = (E_idx.float() - ii).unsqueeze(-1)
# Original Transformer frequencies
frequency = torch.exp(
torch.arange(0, self.num_embeddings, 2, dtype=torch.float32)
* -(np.log(10000.0) / self.num_embeddings)).to(device)
angles = d * frequency.view((1,1,1,-1))
E = torch.cat((torch.cos(angles), torch.sin(angles)), -1)
return E # [N_batch, N_nodes, N_neighbors, num_embeddings]
class EdgeFeatures(nn.Module):
def __init__(self, edge_features, num_positional_embeddings=16,
num_rbf=16, top_k=30, augment_eps=0.):
super(EdgeFeatures, self).__init__()
self.top_k = top_k
self.augment_eps = augment_eps
self.num_rbf = num_rbf
# Positional encoding
self.PE = PositionalEncodings(num_positional_embeddings)
# Embedding and normalization
self.edge_embedding = nn.Linear(num_positional_embeddings + num_rbf + 7, edge_features, bias=True)
self.norm_edges = Normalize(edge_features)
def _dist(self, X, mask, eps=1E-6):
""" Pairwise euclidean distances """
mask_2D = torch.unsqueeze(mask,1) * torch.unsqueeze(mask,2) # mask [N, L] => mask_2D [N, L, L]
dX = torch.unsqueeze(X,1) - torch.unsqueeze(X,2) # X 坐标矩阵 [N, L, 3] dX 坐标差矩阵 [N, L, L, 3]
D = mask_2D * torch.sqrt(torch.sum(dX**2, 3) + eps) # 距离矩阵 [N, L, L]
# Identify k nearest neighbors (including self)
D_max, _ = torch.max(D, -1, keepdim=True)
D_adjust = D + (1. - mask_2D) * D_max
D_neighbors, E_idx = torch.topk(D_adjust, self.top_k, dim=-1, largest=False) # [N, L, k] D_neighbors为具体距离值（从小到大），E_idx为对应邻居节点的编号
return D_neighbors, E_idx
def _rbf(self, D):
# Distance radial basis function
D_min, D_max, D_count = 0., 20., self.num_rbf
D_mu = torch.linspace(D_min, D_max, D_count, device=D.device)
D_mu = D_mu.view([1,1,1,-1])
D_sigma = (D_max - D_min) / D_count
D_expand = torch.unsqueeze(D, -1)
RBF = torch.exp(-((D_expand - D_mu) / D_sigma)**2)
return RBF # [B, L, K, self.num_rbf]
def _quaternions(self, R):
""" Convert a batch of 3D rotations [R] to quaternions [Q]
R [...,3,3]
Q [...,4]
"""
# Simple Wikipedia version
# en.wikipedia.org/wiki/Rotation_matrix#Quaternion
# For other options see math.stackexchange.com/questions/2074316/calculating-rotation-axis-from-rotation-matrix
diag = torch.diagonal(R, dim1=-2, dim2=-1)
Rxx, Ryy, Rzz = diag.unbind(-1)
magnitudes = 0.5 * torch.sqrt(torch.abs(1 + torch.stack([
Rxx - Ryy - Rzz,
- Rxx + Ryy - Rzz,
- Rxx - Ryy + Rzz
], -1)))
_R = lambda i,j: R[:,:,:,i,j]
signs = torch.sign(torch.stack([
_R(2,1) - _R(1,2),
_R(0,2) - _R(2,0),
_R(1,0) - _R(0,1)
], -1))
xyz = signs * magnitudes
# The relu enforces a non-negative trace
w = torch.sqrt(F.relu(1 + diag.sum(-1, keepdim=True))) / 2.
Q = torch.cat((xyz, w), -1)
Q = F.normalize(Q, dim=-1)
return Q
def _orientations(self, X, E_idx, eps=1e-6):
# Shifted slices of unit vectors
dX = X[:,1:,:] - X[:,:-1,:]
U = F.normalize(dX, dim=-1) # 少了第一个（u0）
u_2 = U[:,:-2,:] # u 1~n-2
u_1 = U[:,1:-1,:] # u 2~n-1
# Backbone normals
n_2 = F.normalize(torch.cross(u_2, u_1), dim=-1) # n 1~n-2
# Build relative orientations
o_1 = F.normalize(u_2 - u_1, dim=-1) # b 角平分线向量
O = torch.stack((o_1, n_2, torch.cross(o_1, n_2)), 2)
O = O.view(list(O.shape[:2]) + [9])
O = F.pad(O, (0,0,1,2), 'constant', 0) # [B, L, 9]
O_neighbors = gather_nodes(O, E_idx) # [B, L, K, 9]
X_neighbors = gather_nodes(X, E_idx) # [B, L, K, 3]
# Re-view as rotation matrices
O = O.view(list(O.shape[:2]) + [3,3]) # [B, L, 3, 3]
O_neighbors = O_neighbors.view(list(O_neighbors.shape[:3]) + [3,3]) # [B, L, K, 3, 3]
# Rotate into local reference frames
dX = X_neighbors - X.unsqueeze(-2) # [B, L, K, 3]
dU = torch.matmul(O.unsqueeze(2), dX.unsqueeze(-1)).squeeze(-1) # [B, L, K, 3]
dU = F.normalize(dU, dim=-1)
R = torch.matmul(O.unsqueeze(2).transpose(-1,-2), O_neighbors) # [B, L, K, 3, 3]
Q = self._quaternions(R) # [B, L, K, 4]
# Orientation features
O_features = torch.cat((dU,Q), dim=-1) # [B, L, K, 7]
return O_features
def forward(self, X, mask): # X:[B, L, 3] mask:[B, L]
# Data augmentation
if self.training and self.augment_eps > 0:
X = X + self.augment_eps * torch.randn_like(X)
# Build k-Nearest Neighbors graph
D_neighbors, E_idx = self._dist(X, mask)
# Pairwise features
RBF = self._rbf(D_neighbors)
O_features = self._orientations(X, E_idx)
# Pairwise embeddings
E_positional = self.PE(E_idx)
E = torch.cat((E_positional, RBF, O_features), -1)
E = self.edge_embedding(E)
E = self.norm_edges(E)
return E, E_idx # E [B, L, K, d]; E_idx [B, L, K]
|