在如下例子中，我们使用两种协同过滤神经网络在<用户-物品>二分图中执行物品推荐任务。
- NGCF (:py:class:`dhg.models.GCN`), Neural Graph Collaborative Filtering 论文 (SIGIR 2019).
- LightGCN (:py:class:`dhg.models.LightGCN`), LightGCN: Lightweight Graph Convolutional Networks 论文 (SIGIR 2020).
Gowalla (:py:class:`dhg.data.Gowalla`) 是为<用户-物品>推荐任务收集的数据集。用户的位置被视为物品。 数据集的全集来自于 此网站 。
| 模型 | 测试集上的 NDCG@20 | 测试集上的 Recall@20 |
|---|---|---|
| NGCF | 0.1307 | 0.1547 |
| LightGCN | 0.1550 | 0.1830 |
import time
from copy import deepcopy
import torch
import torch.nn as nn
from torch.utils.data import DataLoader
from dhg import BiGraph
from dhg.data import Gowalla
from dhg.models import NGCF
from dhg.nn import BPRLoss, EmbeddingRegularization
from dhg.metrics import UserItemRecommenderEvaluator as Evaluator
from dhg.random import set_seed
from dhg.utils import UserItemDataset, adj_list_to_edge_listclass BPR_Reg(nn.Module):
def __init__(self, weight_decay):
super().__init__()
self.reg = EmbeddingRegularization(p=2, weight_decay=weight_decay)
self.bpr = BPRLoss(activation="softplus")
def forward(self, emb_users, emb_items, users, pos_items, neg_items, raw_emb_users, raw_emb_items):
cur_u = emb_users[users]
cur_pos_i, cur_neg_i = emb_items[pos_items], emb_items[neg_items]
pos_scores, neg_scores = (cur_u * cur_pos_i).sum(dim=1), (cur_u * cur_neg_i).sum(dim=1)
loss_bpr = self.bpr(pos_scores, neg_scores)
raw_u = raw_emb_users[users]
raw_pos_i, raw_neg_i = raw_emb_items[pos_items], raw_emb_items[neg_items]
loss_l2 = self.reg(raw_u, raw_pos_i, raw_neg_i)
loss = loss_bpr + loss_l2
return loss
def train(net, data_loader, optimizer, criterion, epoch):
net.train()
loss_mean, st = 0, time.time()
for users, pos_items, neg_items in data_loader:
users, pos_items, neg_items = users.to(device), pos_items.to(device), neg_items.to(device)
optimizer.zero_grad()
emb_users, emb_items = net(ui_bigraph)
loss = criterion(
emb_users, emb_items, users, pos_items, neg_items, net.u_embedding.weight, net.i_embedding.weight,
)
loss.backward()
optimizer.step()
loss_mean += loss.item() * users.shape[0]
loss_mean /= len(data_loader.dataset)
print(f"Epoch: {epoch}, Time: {time.time()-st:.5f}s, Loss: {loss_mean:.5f}")
@torch.no_grad()
def validate(net, data_loader):
net.eval()
for users, train_mask, true_rating in data_loader:
users, train_mask, true_rating = (
users.to(device),
train_mask.to(device),
true_rating.to(device),
)
emb_users, emb_items = net(ui_bigraph)
pred_rating = emb_users[users] @ emb_items.t()
pred_rating += train_mask
evaluator.validate_add_batch(true_rating, pred_rating)
return evaluator.validate_epoch_res()
@torch.no_grad()
def test(net, data_loader):
net.eval()
for users, train_mask, true_rating in data_loader:
users, train_mask, true_rating = (
users.to(device),
train_mask.to(device),
true_rating.to(device),
)
emb_users, emb_items = net(ui_bigraph)
pred_rating = emb_users[users] @ emb_items.t()
pred_rating += train_mask
evaluator.test_add_batch(true_rating, pred_rating)
return evaluator.test_epoch_res()Note
更多关于评测器 Evaluator 的细节可以参照 :doc:`构建指标评测器 </zh/tutorial/metric>` 章节。
if __name__ == "__main__":
dim_emb = 64
lr = 0.001
num_workers = 0
batch_sz = 2048
val_freq = 20
epoch_max = 1000
weight_decay = 1e-4
set_seed(2022)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
evaluator = Evaluator([{"ndcg": {"k": 20}}, {"recall": {"k": 20}}])
data = Gowalla()
num_u, num_i = data["num_users"], data["num_items"]
train_adj_list = data["train_adj_list"]
test_adj_list = data["test_adj_list"]
ui_bigraph = BiGraph.from_adj_list(num_u, num_i, train_adj_list)
ui_bigraph = ui_bigraph.to(device)
train_edge_list = adj_list_to_edge_list(train_adj_list)
test_edge_list = adj_list_to_edge_list(test_adj_list)
train_dataset = UserItemDataset(num_u, num_i, train_edge_list)
test_dataset = UserItemDataset(num_u, num_i, test_edge_list, train_user_item_list=train_edge_list, phase="test")
train_loader = DataLoader(train_dataset, batch_size=batch_sz, shuffle=True, num_workers=num_workers)
test_loader = DataLoader(test_dataset, batch_size=batch_sz, shuffle=False, num_workers=num_workers)
net = NGCF(num_u, num_i, dim_emb)
net = net.to(device)
criterion = BPR_Reg(weight_decay)
optimizer = torch.optim.Adam(net.parameters(), lr=lr)
best_state, best_val, best_epoch = None, 0, -1
for epoch in range(epoch_max):
train(net, train_loader, optimizer, criterion, epoch)
if epoch % val_freq == 0:
val_res = validate(net, test_loader)
print(f"Validation: NDCG@20 -> {val_res}")
if val_res > best_val:
best_epoch = epoch
best_val = val_res
best_state = deepcopy(net.state_dict())
print("train finished")
print(f"best val: {best_val}")
print(f"best epoch: {best_epoch}")
print("testing...")
net.load_state_dict(best_state)
test_res = test(net, test_loader)
print(f"test res: {test_res}").. only:: not latex
输出
^^^^^^^^^^^
.. code-block::
Epoch: 0, Time: 17.58267s, Loss: 0.57975
Validation: NDCG@20 -> 0.059597898178090525
Epoch: 1, Time: 17.35420s, Loss: 0.53948
Epoch: 2, Time: 16.67790s, Loss: 0.49900
Epoch: 3, Time: 16.58108s, Loss: 0.45402
Epoch: 4, Time: 16.49324s, Loss: 0.41055
Epoch: 5, Time: 16.47659s, Loss: 0.37169
Epoch: 6, Time: 16.50014s, Loss: 0.33842
Epoch: 7, Time: 16.53070s, Loss: 0.31066
Epoch: 8, Time: 16.50077s, Loss: 0.28642
Epoch: 9, Time: 16.47511s, Loss: 0.26709
Epoch: 10, Time: 16.48582s, Loss: 0.25038
Epoch: 11, Time: 16.48268s, Loss: 0.23593
Epoch: 12, Time: 16.55598s, Loss: 0.22323
Epoch: 13, Time: 16.59955s, Loss: 0.21264
Epoch: 14, Time: 16.57648s, Loss: 0.20171
Epoch: 15, Time: 16.61875s, Loss: 0.19399
Epoch: 16, Time: 16.60113s, Loss: 0.18529
Epoch: 17, Time: 16.67147s, Loss: 0.17826
Epoch: 18, Time: 16.39420s, Loss: 0.17196
Epoch: 19, Time: 16.43819s, Loss: 0.16577
Epoch: 20, Time: 16.39095s, Loss: 0.16056
Validation: NDCG@20 -> 0.0796889192830519
Epoch: 21, Time: 16.38881s, Loss: 0.15489
Epoch: 22, Time: 16.38985s, Loss: 0.15104
Epoch: 23, Time: 16.34736s, Loss: 0.14618
Epoch: 24, Time: 16.45004s, Loss: 0.14248
Epoch: 25, Time: 16.47847s, Loss: 0.13837
Epoch: 26, Time: 16.37476s, Loss: 0.13460
Epoch: 27, Time: 16.39726s, Loss: 0.13152
Epoch: 28, Time: 16.46616s, Loss: 0.12831
Epoch: 29, Time: 16.42933s, Loss: 0.12524
Epoch: 30, Time: 16.42688s, Loss: 0.12196
Epoch: 31, Time: 16.39388s, Loss: 0.11980
Epoch: 32, Time: 16.45209s, Loss: 0.11667
Epoch: 33, Time: 16.38611s, Loss: 0.11485
Epoch: 34, Time: 16.38676s, Loss: 0.11186
Epoch: 35, Time: 16.43171s, Loss: 0.11052
Epoch: 36, Time: 16.42350s, Loss: 0.10853
Epoch: 37, Time: 16.46971s, Loss: 0.10643
Epoch: 38, Time: 16.41361s, Loss: 0.10481
Epoch: 39, Time: 16.40113s, Loss: 0.10274
Epoch: 40, Time: 16.45297s, Loss: 0.10065
Validation: NDCG@20 -> 0.09484630939006403
Epoch: 41, Time: 16.20096s, Loss: 0.09951
Epoch: 42, Time: 16.33159s, Loss: 0.09786
Epoch: 43, Time: 16.41295s, Loss: 0.09629
Epoch: 44, Time: 16.29521s, Loss: 0.09473
Epoch: 45, Time: 16.31462s, Loss: 0.09310
Epoch: 46, Time: 16.30070s, Loss: 0.09155
Epoch: 47, Time: 16.42125s, Loss: 0.09050
Epoch: 48, Time: 16.34268s, Loss: 0.08982
Epoch: 49, Time: 16.38188s, Loss: 0.08804
Epoch: 50, Time: 16.35001s, Loss: 0.08735
Epoch: 51, Time: 16.30478s, Loss: 0.08568
Epoch: 52, Time: 16.26564s, Loss: 0.08473
Epoch: 53, Time: 16.38207s, Loss: 0.08340
Epoch: 54, Time: 16.34952s, Loss: 0.08275
Epoch: 55, Time: 16.41525s, Loss: 0.08166
Epoch: 56, Time: 16.34333s, Loss: 0.08030
Epoch: 57, Time: 16.43872s, Loss: 0.07994
Epoch: 58, Time: 16.37634s, Loss: 0.07892
Epoch: 59, Time: 16.37193s, Loss: 0.07846
Epoch: 60, Time: 16.36561s, Loss: 0.07732
Validation: NDCG@20 -> 0.10073506573468528
Epoch: 61, Time: 16.31512s, Loss: 0.07683
Epoch: 62, Time: 16.48562s, Loss: 0.07560
Epoch: 63, Time: 16.38161s, Loss: 0.07542
Epoch: 64, Time: 16.38181s, Loss: 0.07415
Epoch: 65, Time: 16.37734s, Loss: 0.07392
Epoch: 66, Time: 16.35093s, Loss: 0.07365
Epoch: 67, Time: 16.42241s, Loss: 0.07198
Epoch: 68, Time: 16.39753s, Loss: 0.07206
Epoch: 69, Time: 16.43910s, Loss: 0.07088
Epoch: 70, Time: 16.40806s, Loss: 0.07004
Epoch: 71, Time: 16.38006s, Loss: 0.07041
Epoch: 72, Time: 16.42882s, Loss: 0.06922
Epoch: 73, Time: 16.41414s, Loss: 0.06855
Epoch: 74, Time: 16.34444s, Loss: 0.06793
Epoch: 75, Time: 16.40675s, Loss: 0.06769
Epoch: 76, Time: 16.41324s, Loss: 0.06697
Epoch: 77, Time: 16.38147s, Loss: 0.06661
Epoch: 78, Time: 16.42382s, Loss: 0.06648
Epoch: 79, Time: 16.41072s, Loss: 0.06594
Epoch: 80, Time: 16.38907s, Loss: 0.06481
Validation: NDCG@20 -> 0.10532317576637099
Epoch: 81, Time: 16.42970s, Loss: 0.06468
Epoch: 82, Time: 16.45658s, Loss: 0.06442
Epoch: 83, Time: 16.38556s, Loss: 0.06388
Epoch: 84, Time: 16.32818s, Loss: 0.06370
Epoch: 85, Time: 16.36058s, Loss: 0.06294
Epoch: 86, Time: 16.34388s, Loss: 0.06260
Epoch: 87, Time: 16.33080s, Loss: 0.06234
Epoch: 88, Time: 16.36727s, Loss: 0.06197
Epoch: 89, Time: 16.32790s, Loss: 0.06154
Epoch: 90, Time: 16.43729s, Loss: 0.06101
Epoch: 91, Time: 16.38772s, Loss: 0.06070
Epoch: 92, Time: 16.42943s, Loss: 0.06037
Epoch: 93, Time: 16.36849s, Loss: 0.06043
Epoch: 94, Time: 16.39440s, Loss: 0.05969
Epoch: 95, Time: 16.33486s, Loss: 0.05954
Epoch: 96, Time: 16.34549s, Loss: 0.05876
Epoch: 97, Time: 16.37610s, Loss: 0.05866
Epoch: 98, Time: 16.39110s, Loss: 0.05857
Epoch: 99, Time: 16.38359s, Loss: 0.05788
Epoch: 100, Time: 16.42878s, Loss: 0.05773
Validation: NDCG@20 -> 0.10774315184649631
Epoch: 101, Time: 16.37178s, Loss: 0.05742
Epoch: 102, Time: 16.50821s, Loss: 0.05743
Epoch: 103, Time: 16.38737s, Loss: 0.05706
Epoch: 104, Time: 16.38123s, Loss: 0.05672
Epoch: 105, Time: 16.38323s, Loss: 0.05625
Epoch: 106, Time: 16.39332s, Loss: 0.05609
Epoch: 107, Time: 16.38817s, Loss: 0.05554
Epoch: 108, Time: 16.39039s, Loss: 0.05561
Epoch: 109, Time: 16.40110s, Loss: 0.05534
Epoch: 110, Time: 16.42629s, Loss: 0.05496
Epoch: 111, Time: 16.40456s, Loss: 0.05436
Epoch: 112, Time: 16.42960s, Loss: 0.05448
Epoch: 113, Time: 16.41036s, Loss: 0.05448
Epoch: 114, Time: 16.38433s, Loss: 0.05405
Epoch: 115, Time: 16.38922s, Loss: 0.05338
Epoch: 116, Time: 16.37122s, Loss: 0.05375
Epoch: 117, Time: 16.39454s, Loss: 0.05359
Epoch: 118, Time: 16.37232s, Loss: 0.05301
Epoch: 119, Time: 16.38497s, Loss: 0.05317
Epoch: 120, Time: 16.44990s, Loss: 0.05326
Validation: NDCG@20 -> 0.11050138281284864
Epoch: 121, Time: 16.42819s, Loss: 0.05270
Epoch: 122, Time: 16.43767s, Loss: 0.05240
Epoch: 123, Time: 16.33994s, Loss: 0.05205
Epoch: 124, Time: 16.37961s, Loss: 0.05193
Epoch: 125, Time: 16.40023s, Loss: 0.05187
Epoch: 126, Time: 16.44434s, Loss: 0.05143
Epoch: 127, Time: 16.44631s, Loss: 0.05155
Epoch: 128, Time: 16.42970s, Loss: 0.05141
Epoch: 129, Time: 16.43539s, Loss: 0.05119
Epoch: 130, Time: 16.41379s, Loss: 0.05097
Epoch: 131, Time: 16.43115s, Loss: 0.05080
Epoch: 132, Time: 16.41100s, Loss: 0.05077
Epoch: 133, Time: 16.42312s, Loss: 0.05043
Epoch: 134, Time: 16.39068s, Loss: 0.05028
Epoch: 135, Time: 16.37832s, Loss: 0.05016
Epoch: 136, Time: 16.39196s, Loss: 0.04994
Epoch: 137, Time: 16.38732s, Loss: 0.04976
Epoch: 138, Time: 16.41807s, Loss: 0.04935
Epoch: 139, Time: 16.37651s, Loss: 0.04916
Epoch: 140, Time: 16.39615s, Loss: 0.04923
Validation: NDCG@20 -> 0.11280099123452347
Epoch: 141, Time: 16.41225s, Loss: 0.04903
Epoch: 142, Time: 16.46800s, Loss: 0.04892
Epoch: 143, Time: 16.39678s, Loss: 0.04835
Epoch: 144, Time: 16.38563s, Loss: 0.04838
Epoch: 145, Time: 16.37892s, Loss: 0.04874
Epoch: 146, Time: 16.46196s, Loss: 0.04824
Epoch: 147, Time: 16.39248s, Loss: 0.04801
Epoch: 148, Time: 16.37935s, Loss: 0.04801
Epoch: 149, Time: 16.44855s, Loss: 0.04773
Epoch: 150, Time: 16.94777s, Loss: 0.04736
Epoch: 151, Time: 17.25382s, Loss: 0.04770
Epoch: 152, Time: 17.55223s, Loss: 0.04734
Epoch: 153, Time: 17.03791s, Loss: 0.04729
Epoch: 154, Time: 17.59021s, Loss: 0.04759
Epoch: 155, Time: 17.50267s, Loss: 0.04705
Epoch: 156, Time: 17.43284s, Loss: 0.04690
Epoch: 157, Time: 16.67660s, Loss: 0.04659
Epoch: 158, Time: 17.15853s, Loss: 0.04668
Epoch: 159, Time: 16.93252s, Loss: 0.04653
Epoch: 160, Time: 16.66944s, Loss: 0.04636
Validation: NDCG@20 -> 0.11396838930066855
Epoch: 161, Time: 16.75059s, Loss: 0.04627
Epoch: 162, Time: 16.80186s, Loss: 0.04613
Epoch: 163, Time: 16.75320s, Loss: 0.04616
Epoch: 164, Time: 16.79349s, Loss: 0.04604
Epoch: 165, Time: 16.82817s, Loss: 0.04579
Epoch: 166, Time: 16.78084s, Loss: 0.04599
Epoch: 167, Time: 16.83057s, Loss: 0.04553
Epoch: 168, Time: 16.83778s, Loss: 0.04554
Epoch: 169, Time: 16.83636s, Loss: 0.04548
Epoch: 170, Time: 16.76483s, Loss: 0.04547
Epoch: 171, Time: 16.85442s, Loss: 0.04487
Epoch: 172, Time: 16.83118s, Loss: 0.04475
Epoch: 173, Time: 16.80676s, Loss: 0.04518
Epoch: 174, Time: 16.82507s, Loss: 0.04470
Epoch: 175, Time: 16.87042s, Loss: 0.04485
Epoch: 176, Time: 17.00146s, Loss: 0.04471
Epoch: 177, Time: 17.02007s, Loss: 0.04455
Epoch: 178, Time: 16.63682s, Loss: 0.04445
Epoch: 179, Time: 17.08953s, Loss: 0.04450
Epoch: 180, Time: 16.89926s, Loss: 0.04419
Validation: NDCG@20 -> 0.11516925413130324
import time
from copy import deepcopy
import torch
import torch.nn as nn
from torch.utils.data import DataLoader
from dhg import BiGraph
from dhg.data import Gowalla
from dhg.models import LightGCN
from dhg.nn import BPRLoss, EmbeddingRegularization
from dhg.metrics import UserItemRecommenderEvaluator as Evaluator
from dhg.random import set_seed
from dhg.utils import UserItemDataset, adj_list_to_edge_listclass BPR_Reg(nn.Module):
def __init__(self, weight_decay):
super().__init__()
self.reg = EmbeddingRegularization(p=2, weight_decay=weight_decay)
self.bpr = BPRLoss(activation="softplus")
def forward(self, emb_users, emb_items, users, pos_items, neg_items, raw_emb_users, raw_emb_items):
cur_u = emb_users[users]
cur_pos_i, cur_neg_i = emb_items[pos_items], emb_items[neg_items]
pos_scores, neg_scores = (cur_u * cur_pos_i).sum(dim=1), (cur_u * cur_neg_i).sum(dim=1)
loss_bpr = self.bpr(pos_scores, neg_scores)
raw_u = raw_emb_users[users]
raw_pos_i, raw_neg_i = raw_emb_items[pos_items], raw_emb_items[neg_items]
loss_l2 = self.reg(raw_u, raw_pos_i, raw_neg_i)
loss = loss_bpr + loss_l2
return loss
def train(net, data_loader, optimizer, criterion, epoch):
net.train()
loss_mean, st = 0, time.time()
for users, pos_items, neg_items in data_loader:
users, pos_items, neg_items = users.to(device), pos_items.to(device), neg_items.to(device)
optimizer.zero_grad()
emb_users, emb_items = net(ui_bigraph)
loss = criterion(
emb_users, emb_items, users, pos_items, neg_items, net.u_embedding.weight, net.i_embedding.weight,
)
loss.backward()
optimizer.step()
loss_mean += loss.item() * users.shape[0]
loss_mean /= len(data_loader.dataset)
print(f"Epoch: {epoch}, Time: {time.time()-st:.5f}s, Loss: {loss_mean:.5f}")
@torch.no_grad()
def validate(net, data_loader):
net.eval()
for users, train_mask, true_rating in data_loader:
users, train_mask, true_rating = (
users.to(device),
train_mask.to(device),
true_rating.to(device),
)
emb_users, emb_items = net(ui_bigraph)
pred_rating = emb_users[users] @ emb_items.t()
pred_rating += train_mask
evaluator.validate_add_batch(true_rating, pred_rating)
return evaluator.validate_epoch_res()
@torch.no_grad()
def test(net, data_loader):
net.eval()
for users, train_mask, true_rating in data_loader:
users, train_mask, true_rating = (
users.to(device),
train_mask.to(device),
true_rating.to(device),
)
emb_users, emb_items = net(ui_bigraph)
pred_rating = emb_users[users] @ emb_items.t()
pred_rating += train_mask
evaluator.test_add_batch(true_rating, pred_rating)
return evaluator.test_epoch_res()Note
更多关于评测器 Evaluator 的细节可以参照 :doc:`构建指标评测器 </zh/tutorial/metric>` 章节。
if __name__ == "__main__":
dim_emb = 64
lr = 0.001
num_workers = 0
batch_sz = 2048
val_freq = 20
epoch_max = 1000
weight_decay = 1e-4
set_seed(2022)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
evaluator = Evaluator([{"ndcg": {"k": 20}}, {"recall": {"k": 20}}])
data = Gowalla()
num_u, num_i = data["num_users"], data["num_items"]
train_adj_list = data["train_adj_list"]
test_adj_list = data["test_adj_list"]
ui_bigraph = BiGraph.from_adj_list(num_u, num_i, train_adj_list)
ui_bigraph = ui_bigraph.to(device)
train_edge_list = adj_list_to_edge_list(train_adj_list)
test_edge_list = adj_list_to_edge_list(test_adj_list)
train_dataset = UserItemDataset(num_u, num_i, train_edge_list)
test_dataset = UserItemDataset(num_u, num_i, test_edge_list, train_user_item_list=train_edge_list, phase="test")
train_loader = DataLoader(train_dataset, batch_size=batch_sz, shuffle=True, num_workers=num_workers)
test_loader = DataLoader(test_dataset, batch_size=batch_sz, shuffle=False, num_workers=num_workers)
net = LightGCN(num_u, num_i, dim_emb)
net = net.to(device)
criterion = BPR_Reg(weight_decay)
optimizer = torch.optim.Adam(net.parameters(), lr=lr)
best_state, best_val, best_epoch = None, 0, -1
for epoch in range(epoch_max):
train(net, train_loader, optimizer, criterion, epoch)
if epoch % val_freq == 0:
val_res = validate(net, test_loader)
print(f"Validation: NDCG@20 -> {val_res}")
if val_res > best_val:
best_epoch = epoch
best_val = val_res
best_state = deepcopy(net.state_dict())
print("train finished")
print(f"best val: {best_val}")
print(f"best epoch: {best_epoch}")
print("testing...")
net.load_state_dict(best_state)
test_res = test(net, test_loader)
print(f"test res: {test_res}").. only:: not latex
输出
^^^^^^^^^^^
.. code-block::
Epoch: 0, Time: 13.99548s, Loss: 0.50885
Validation: 0.06785113136172075
Epoch: 1, Time: 13.64900s, Loss: 0.23104
Epoch: 2, Time: 14.04344s, Loss: 0.17122
Epoch: 3, Time: 14.17638s, Loss: 0.14329
Epoch: 4, Time: 14.00283s, Loss: 0.12590
Epoch: 5, Time: 13.74365s, Loss: 0.11401
Epoch: 6, Time: 13.84788s, Loss: 0.10609
Epoch: 7, Time: 13.74667s, Loss: 0.09946
Epoch: 8, Time: 13.52109s, Loss: 0.09344
Epoch: 9, Time: 13.36949s, Loss: 0.08926
Epoch: 10, Time: 13.38029s, Loss: 0.08551
Epoch: 11, Time: 13.34837s, Loss: 0.08222
Epoch: 12, Time: 13.35350s, Loss: 0.08036
Epoch: 13, Time: 13.40274s, Loss: 0.07683
Epoch: 14, Time: 13.40829s, Loss: 0.07503
Epoch: 15, Time: 12.97056s, Loss: 0.07243
Epoch: 16, Time: 12.99591s, Loss: 0.07044
Epoch: 17, Time: 13.00338s, Loss: 0.06855
Epoch: 18, Time: 12.99054s, Loss: 0.06646
Epoch: 19, Time: 12.99395s, Loss: 0.06438
Epoch: 20, Time: 12.98960s, Loss: 0.06309
Validation: 0.11326732434508542
Epoch: 21, Time: 12.86631s, Loss: 0.06106
Epoch: 22, Time: 12.91743s, Loss: 0.06020
Epoch: 23, Time: 12.98517s, Loss: 0.05888
Epoch: 24, Time: 12.94291s, Loss: 0.05717
Epoch: 25, Time: 13.02582s, Loss: 0.05655
Epoch: 26, Time: 13.63684s, Loss: 0.05494
Epoch: 27, Time: 13.43329s, Loss: 0.05417
Epoch: 28, Time: 13.40190s, Loss: 0.05334
Epoch: 29, Time: 13.34597s, Loss: 0.05158
Epoch: 30, Time: 13.39115s, Loss: 0.05144
Epoch: 31, Time: 13.36618s, Loss: 0.05128
Epoch: 32, Time: 13.39683s, Loss: 0.04959
Epoch: 33, Time: 13.35201s, Loss: 0.04861
Epoch: 34, Time: 13.36965s, Loss: 0.04781
Epoch: 35, Time: 13.66474s, Loss: 0.04725
Epoch: 36, Time: 14.06111s, Loss: 0.04681
Epoch: 37, Time: 13.79196s, Loss: 0.04575
Epoch: 38, Time: 13.82344s, Loss: 0.04595
Epoch: 39, Time: 13.98216s, Loss: 0.04427
Epoch: 40, Time: 14.05523s, Loss: 0.04426
Validation: 0.12357260732699984
Epoch: 41, Time: 13.36727s, Loss: 0.04292
Epoch: 42, Time: 13.37445s, Loss: 0.04322
Epoch: 43, Time: 13.38032s, Loss: 0.04226
Epoch: 44, Time: 13.40528s, Loss: 0.04133
Epoch: 45, Time: 14.11705s, Loss: 0.04139
Epoch: 46, Time: 13.51289s, Loss: 0.04059
Epoch: 47, Time: 13.63507s, Loss: 0.03985
Epoch: 48, Time: 13.82129s, Loss: 0.03967
Epoch: 49, Time: 13.38149s, Loss: 0.03917
Epoch: 50, Time: 13.61731s, Loss: 0.03890
Epoch: 51, Time: 13.77848s, Loss: 0.03834
Epoch: 52, Time: 13.78244s, Loss: 0.03772
Epoch: 53, Time: 13.53519s, Loss: 0.03744
Epoch: 54, Time: 13.56650s, Loss: 0.03690
Epoch: 55, Time: 13.77765s, Loss: 0.03633
Epoch: 56, Time: 13.55891s, Loss: 0.03594
Epoch: 57, Time: 13.82406s, Loss: 0.03581
Epoch: 58, Time: 13.62316s, Loss: 0.03546
Epoch: 59, Time: 13.86439s, Loss: 0.03511
Epoch: 60, Time: 13.75384s, Loss: 0.03478
Validation: 0.13109645468633707
Epoch: 61, Time: 14.04090s, Loss: 0.03443
Epoch: 62, Time: 13.59308s, Loss: 0.03342
Epoch: 63, Time: 13.47868s, Loss: 0.03315
Epoch: 64, Time: 13.58020s, Loss: 0.03313
Epoch: 65, Time: 13.78613s, Loss: 0.03299
Epoch: 66, Time: 14.13540s, Loss: 0.03287
Epoch: 67, Time: 13.88064s, Loss: 0.03239
Epoch: 68, Time: 14.19946s, Loss: 0.03220
Epoch: 69, Time: 13.85164s, Loss: 0.03172
Epoch: 70, Time: 13.80321s, Loss: 0.03161
Epoch: 71, Time: 13.59180s, Loss: 0.03125
Epoch: 72, Time: 13.57149s, Loss: 0.03068
Epoch: 73, Time: 13.87281s, Loss: 0.03073
Epoch: 74, Time: 13.98456s, Loss: 0.03003
Epoch: 75, Time: 13.83081s, Loss: 0.03033
Epoch: 76, Time: 13.60854s, Loss: 0.02954
Epoch: 77, Time: 13.74393s, Loss: 0.02925
Epoch: 78, Time: 13.82418s, Loss: 0.02909
Epoch: 79, Time: 13.55567s, Loss: 0.02887
Epoch: 80, Time: 13.39723s, Loss: 0.02884
Validation: 0.13620756897343958
Epoch: 81, Time: 13.87684s, Loss: 0.02881
Epoch: 82, Time: 13.72004s, Loss: 0.02830
Epoch: 83, Time: 13.52762s, Loss: 0.02796
Epoch: 84, Time: 13.50852s, Loss: 0.02777
Epoch: 85, Time: 13.65227s, Loss: 0.02762
Epoch: 86, Time: 13.84981s, Loss: 0.02752
Epoch: 87, Time: 14.03578s, Loss: 0.02743
Epoch: 88, Time: 13.86019s, Loss: 0.02709
Epoch: 89, Time: 14.47703s, Loss: 0.02670
Epoch: 90, Time: 13.90316s, Loss: 0.02669
Epoch: 91, Time: 13.85412s, Loss: 0.02622
Epoch: 92, Time: 14.55231s, Loss: 0.02636
Epoch: 93, Time: 14.12314s, Loss: 0.02616
Epoch: 94, Time: 14.14073s, Loss: 0.02643
Epoch: 95, Time: 14.76731s, Loss: 0.02528
Epoch: 96, Time: 13.95123s, Loss: 0.02558
Epoch: 97, Time: 13.58211s, Loss: 0.02548
Epoch: 98, Time: 14.17444s, Loss: 0.02538
Epoch: 99, Time: 14.03820s, Loss: 0.02530
Epoch: 100, Time: 13.79881s, Loss: 0.02477
Validation: 0.14007331335739823
Epoch: 101, Time: 14.41267s, Loss: 0.02501
Epoch: 102, Time: 13.95937s, Loss: 0.02485
Epoch: 103, Time: 14.02000s, Loss: 0.02445
Epoch: 104, Time: 13.91621s, Loss: 0.02418
Epoch: 105, Time: 13.97738s, Loss: 0.02410
Epoch: 106, Time: 13.94001s, Loss: 0.02383
Epoch: 107, Time: 13.96132s, Loss: 0.02386
Epoch: 108, Time: 13.96773s, Loss: 0.02362
Epoch: 109, Time: 14.00794s, Loss: 0.02350
Epoch: 110, Time: 13.80064s, Loss: 0.02343
Epoch: 111, Time: 14.28152s, Loss: 0.02332
Epoch: 112, Time: 14.38398s, Loss: 0.02308
Epoch: 113, Time: 14.34458s, Loss: 0.02345
Epoch: 114, Time: 14.18515s, Loss: 0.02276
Epoch: 115, Time: 13.56739s, Loss: 0.02268
Epoch: 116, Time: 14.22387s, Loss: 0.02314
Epoch: 117, Time: 14.02960s, Loss: 0.02266
Epoch: 118, Time: 13.98667s, Loss: 0.02241
Epoch: 119, Time: 13.81673s, Loss: 0.02238
Epoch: 120, Time: 13.91288s, Loss: 0.02207
Validation: 0.14275566576589846
Epoch: 121, Time: 14.15440s, Loss: 0.02199
Epoch: 122, Time: 14.28269s, Loss: 0.02178
Epoch: 123, Time: 14.10793s, Loss: 0.02202
Epoch: 124, Time: 14.46924s, Loss: 0.02160
Epoch: 125, Time: 14.01888s, Loss: 0.02190
Epoch: 126, Time: 14.50532s, Loss: 0.02163
Epoch: 127, Time: 13.96982s, Loss: 0.02135
Epoch: 128, Time: 13.80776s, Loss: 0.02115
Epoch: 129, Time: 13.81826s, Loss: 0.02132
Epoch: 130, Time: 13.64502s, Loss: 0.02090
Epoch: 131, Time: 14.08872s, Loss: 0.02094
Epoch: 132, Time: 13.89601s, Loss: 0.02117
Epoch: 133, Time: 13.81755s, Loss: 0.02088
Epoch: 134, Time: 14.06675s, Loss: 0.02075
Epoch: 135, Time: 14.07287s, Loss: 0.02068
Epoch: 136, Time: 14.07303s, Loss: 0.02062
Epoch: 137, Time: 14.07205s, Loss: 0.02035
Epoch: 138, Time: 13.73393s, Loss: 0.02037
Epoch: 139, Time: 14.10216s, Loss: 0.02026
Epoch: 140, Time: 13.71037s, Loss: 0.02014
Validation: 0.14488457332453364