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temp_gntk.py
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import torch
import math
import scipy
import numpy as np
class TemporalGNTK(object):
def __next(self, S, diag_1, diag_2):
S /= (diag_1[:, None] * diag_2[None, :])
S = torch.clamp(S, -1, 1)
dS = (math.pi - torch.arccos(S)) / (math.pi)
S = (S * (math.pi - torch.arccos(S)) + torch.sqrt(1 - S * S)) / (math.pi)
S *= (diag_1[:, None] * diag_2[None, :])
return S, dS
def __next_wo_diag(self, S):
diag = torch.sqrt(S.diag())
S /= (diag[:, None] * diag[None, :])
S = torch.clamp(S, -1, 1)
dS = (math.pi - torch.arccos(S)) / (math.pi)
S = (S * (math.pi - torch.arccos(S)) + torch.sqrt(1 - S * S)) / (math.pi)
S *= (diag[:, None] * diag[None, :])
return S, dS
def normalize_length(self, X):
r"""
Args:
X (torch.tensor): shape [N, K, d]
Returns:
X (torch.tensor): vector length is normalized to 1 in the last dimension
"""
# X: [N, K, d] -> length [N, K, 1]
length = torch.sqrt(torch.sum(X ** 2, dim = -1)).unsqueeze(-1)
length += (length == 0)
# scale vector to length of 1 -> [N, K, d]
return X / length
def temporal_gntk(self, X_1, X_2, args):
r"""
Args:
X_1 (torch.tensor): shape [N, K, d]
X_2 (torch.tensor): shape [N', K', d]
"""
X_1 = self.normalize_length(X_1)
X_2 = self.normalize_length(X_2)
K_1, K_2 = X_1.shape[1], X_2.shape[1]
N_1, N_2 = X_1.shape[0], X_2.shape[0]
# [N, K, d] [N', K', d] -> [N, N', K, K']
sigma_0 = torch.einsum("abd, mnd -> ambn", X_1, X_2)
ntk_0 = torch.clone(sigma_0)
dot_sigma_1, sigma_1 = self.__next(sigma_0)
ntk_1 = ntk_0 * dot_sigma_1 + sigma_1
# [N, N', K, K']
link_ntk = ntk_1
# [N, N']
node_ntk = torch.einsum("mnpq -> mn", link_ntk) / (K_1 * K_2)
# scalar
graph_ntk = torch.sum(node_ntk) / (N_1 * N_2)
return link_ntk, node_ntk, graph_ntk
def temporal_gntk_2(self, X_1, X_2, args):
r"""
Args:
X_1 (torch.tensor): shape [N, K, d]
X_2 (torch.tensor): shape [N', K', d]
"""
X_1 = self.normalize_length(X_1)
X_2 = self.normalize_length(X_2)
K_1, K_2 = X_1.shape[1], X_2.shape[1]
N_1, N_2 = X_1.shape[0], X_2.shape[0]
# [N, K, d] -> [N, 1, d] -> [N, d]
X_1_agg = torch.sum(X_1, dim = 1).squeeze() / K_1
X_2_agg = torch.sum(X_2, dim = 1).squeeze() / K_2
# [N, N']
sigma_0 = torch.mm(X_1_agg, X_2_agg.T) / args.time_dim
ntk_0 = torch.clone(sigma_0)
dot_sigma_1, sigma_1 = self.__next(sigma_0)
ntk_1 = ntk_0 * dot_sigma_1 + sigma_1
graph_ntk = torch.sum(ntk_1) / (N_1 * N_2)
return graph_ntk
def temporal_gntk_3(self, X_1, X_2, args):
X_1 = self.normalize_length(X_1)
X_2 = self.normalize_length(X_2)
K_1, K_2 = X_1.shape[1], X_2.shape[1]
N_1, N_2 = X_1.shape[0], X_2.shape[0]
# [N, K, d] -> [N, 1, d] -> [N, d]
X_1_agg = torch.sum(X_1, dim = 1).squeeze() / K_1
X_2_agg = torch.sum(X_2, dim = 1).squeeze() / K_2
# [N, N']
sigma = torch.mm(X_1_agg, X_2_agg.T) / (args.time_dim)
ntk = torch.clone(sigma)
for _ in range(args.num_mlp_layers):
dot_sigma, sigma = self.__next(sigma)
ntk = ntk * dot_sigma + sigma
node_ntk = ntk
graph_ntk = torch.sum(node_ntk) / (N_1 * N_2)
return graph_ntk, node_ntk
def temporal_gntk_4(self, node_emb_1, node_emb_2, args):
N_1, N_2 = node_emb_1.shape[0], node_emb_2.shape[0]
# [N, d] [N', d] -> [N, N]
node_emb_1 = self.normalize_length(node_emb_1)
node_emb_2 = self.normalize_length(node_emb_2)
sigma = torch.mm(node_emb_1, node_emb_2.T)
# / (args.time_dim)
ntk = torch.clone(sigma)
for _ in range(args.num_mlp_layers):
sigma, dot_sigma = self.__next_wo_diag(sigma)
ntk = ntk * dot_sigma + sigma
graph_ntk = torch.sum(ntk)
# / (N_1 * N_2)
return graph_ntk
def __next_diag(self, S):
diag = torch.sqrt(S.diag())
S /= (diag[:, None] * diag[None, :])
S = torch.clamp(S, -1, 1)
dS = (math.pi - torch.arccos(S)) / (2 * math.pi)
S = (S * (math.pi - torch.arccos(S)) + torch.sqrt(1 - S * S)) / (2 * math.pi)
S *= (diag[:, None] * diag[None, :])
return S, dS, diag
def get_diag_list(self, node_emb, A, args, return_ntk = False):
n = node_emb.shape[0]
node_emb = self.normalize_length(node_emb)
sigma = torch.mm(node_emb, node_emb.T).nan_to_num()
# if n > 1000:
# sparse_A = A.to_sparse_coo()
# row, col = sparse_A.indices()
# vals = sparse_A.values()
# sparse_A = scipy.sparse.coo_array((vals, (row, col)), shape = (n, n))
# adj_block = np.nan_to_num(scipy.sparse.kron(sparse_A, sparse_A)).astype(np.float64)
# sigma = np.nan_to_num(adj_block.dot(sigma.view(-1, 1).numpy()))
# sigma = torch.from_numpy(sigma).view(n, n)
# else:
# adj_block = torch.kron(A, A).nan_to_num()
# sigma = torch.mm(adj_block.to(torch.float), sigma.view(-1, 1)).view(n, n)
# sigma = sigma.nan_to_num()
ntk = torch.clone(sigma).to(args.device)
sigma = sigma.to(args.device)
diag_list = []
for _ in range(args.num_mlp_layers):
sigma, dot_sigma, diag = self.__next_diag(sigma)
sigma = sigma.nan_to_num()
dot_sigma = dot_sigma.nan_to_num()
diag = diag.nan_to_num()
if args.skip_connection:
ntk = ntk * (dot_sigma + 1) + sigma
else:
ntk = ntk * dot_sigma + sigma
ntk = ntk.nan_to_num()
diag_list.append(diag.detach().cpu())
if return_ntk:
return ntk.detach().cpu, diag_list
return diag_list
def gntk(self, node_emb_1, node_emb_2, A_1, A_2, diag_list_1, diag_list_2, args):
n_1, n_2 = node_emb_1.shape[0], node_emb_2.shape[0]
node_emb_1 = self.normalize_length(node_emb_1)
node_emb_2 = self.normalize_length(node_emb_2)
sigma = torch.mm(node_emb_1, node_emb_2.T).nan_to_num()
# if n_1 > 1000 or n_2 > 1000:
# sparse_A_1, sparse_A_2 = A_1.to_sparse_coo(), A_2.to_sparse_coo()
# row, col = sparse_A_1.indices()
# vals = sparse_A_1.values()
# sparse_A_1 = scipy.sparse.coo_array((vals, (row, col)), shape = (n_1, n_1))
# row, col = sparse_A_2.indices()
# vals = sparse_A_2.values()
# sparse_A_2 = scipy.sparse.coo_array((vals, (row, col)), shape = (n_2, n_2))
# adj_block = np.nan_to_num(scipy.sparse.kron(sparse_A_1, sparse_A_2)).astype(np.float64)
# sigma = np.nan_to_num(adj_block.dot(sigma.view(-1, 1).numpy()))
# sigma = torch.from_numpy(sigma).view(n_1, n_2)
# else:
# adj_block = torch.kron(A_1, A_2).nan_to_num()
# sigma = torch.mm(adj_block.to(torch.float), sigma.view(-1, 1)).view(n_1, n_2).nan_to_num()
ntk = torch.clone(sigma).to(args.device)
sigma = sigma.to(args.device)
for i in range(args.num_mlp_layers):
sigma, dot_sigma = self.__next(sigma, diag_list_1[i].to(args.device), diag_list_2[i].to(args.device))
sigma = sigma.nan_to_num()
dot_sigma = dot_sigma.nan_to_num()
if args.skip_connection:
ntk = ntk * (dot_sigma + 1) + sigma
else:
ntk = ntk * dot_sigma + sigma
ntk = ntk.nan_to_num()
if args.node_ntk:
return ntk.detach().cpu()
if args.mean_graph_pooling:
return (torch.sum(ntk) / (n_1 * n_2)).detach().cpu()
return torch.sum(ntk).detach().cpu()