【学习日志】【TCN】时间序列卷积神经网络(1)

2023-11-05

1. ask bing(Temporal Convolutional Network)

问:“我对CNN、RNN、TCN等神经网络没有任何基础,你能直观地给我讲一下TCN的结构、输入输出和原理吗?”
bing对TCN的解释如下:

TCN是一种用于处理序列数据的神经网络,它可以看作是一种特殊的CNN。CNN是一种用于处理图像数据的神经网络,它可以看作是一种特殊的卷积运算。卷积运算就是将一个小的滑动窗口(称为卷积核或过滤器)在一个大的数据(称为输入或特征图)上滑动,并对每个窗口内的数据进行加权求和,得到一个新的数据(称为输出或激活图)。这样就可以提取出输入中的局部特征,并减少参数数量。
TCN与CNN不同之处在于,它只在序列数据的时间维度上进行卷积运算,而不是在空间维度上。这样就可以保持序列数据的时序信息,并且使得输出只依赖于当前及之前的输入,而不会受到未来输入的影响。这种卷积运算称为因果卷积。
TCN还使用了空洞卷积,这是一种在卷积核中插入空白位置(称为膨胀因子)的技术,使得卷积核可以覆盖更长范围的输入,而不增加参数数量。这样就可以增加感受野,即输出能够感知到输入中多远距离的信息。
TCN还使用了残差连接,这是一种将每层输入直接与输出相加(称为跳跃连接)的技术,使得网络可以更容易地学习恒等映射,并防止梯度消失或爆炸。这样就可以构建更深层次的网络,并提高性能。
TCN通常由多个重复模块组成,每个模块包含两个因果空洞卷积层和一个残差连接。每个模块都有自己独立的膨胀因子和过滤器数量。最后一个模块后面还有一个全连接层或者softmax层来输出预测结果。
TCN接收一个多维数组作为输入,其中第一维表示序列长度(即时间步数),第二维表示特征数量(即信号通道数)。例如,在生物信号处理中,如果我们有1000个时间步长和8个信号通道,则我们可以将其表示为一个1000×8 的数组作为TCN 的输入。
TCN输出一个多维数组作为预测结果,其中第一维表示序列长度(即时间步数),第二维表示类别数量(即预测目标数)。例如,在生物信号分类中,如果我们有1000个时间步长和4个类别,则我们可以将其表示为一个1000×4 的数组作为TCN 的输出。

总结一下:

  1. TCN是在CNN基础上衍生的一种神经网络;CNN主要用于处理数字图像,本质是一种特殊的卷积(滤波)运算,且是在空间维度进行的;而FCN使用的是因果卷积,即不是在空间维度进行卷积运算,而是对序列(sequence)数据在时间维度进行卷积运算。
  2. TCN在算法优化上采用了:膨胀因果卷积空洞卷积(通过在卷积核中插入空白位置/膨胀因子,使卷积核覆盖更长范围的输入而不增加参数数量,实现增加感受野)、残差连接(可以构建更深层次的网络、提高性能)。
  3. TCN的结构上由多个重复模块组成,每个模块包含两个因果空洞卷积层+一个残差连接,每个模块的膨胀因子、过滤器数量都不一样;最后一个模块后再加一个全连接层/softmax层来输出预测结果。
  4. TCN输入输出数据:输入数据是一个多维数组,比如处理生物信号的话,第一维度表示信号序列长度/时间步数(取决于采样频率),第二维度表示特征数量/信号通道数(取决于采集了几个通道和特征处理的方法);输出数据也是多维数组,第一维度还是信号序列长度/时间步数,第二维度表示类别数量/预测目标数(比如根据多个通道的生物信号预测关节角度和时间的关系)。

2. 边跑边学

2.1 先跑起来

源码来源文献
源码中包括好几个案例:

The Adding Problem with various T (we evaluated on T=200, 400, 600)
Copying Memory Task with various T (we evaluated on T=500, 1000, 2000)
Sequential MNIST digit classification
Permuted Sequential MNIST (based on Seq. MNIST, but more challenging)
JSB Chorales polyphonic music
Nottingham polyphonic music
PennTreebank [SMALL] word-level language modeling (LM)
Wikitext-103 [LARGE] word-level LM
LAMBADA [LARGE] word-level LM and textual understanding
PennTreebank [MEDIUM] char-level LM
text8 [LARGE] char-level LM

我这里选择了:JSB Chorales polyphonic music和Nottingham polyphonic music,对应poly_music文件夹,因为处理预测声波数据看起来和我要应用的处理生物信号数据比较相近。当然我们可以根据自己的需求选择其他的案例跑。
README中强调了,对应每个案例跑模型时只需要运行[TASK_NAME]_test.py,比如打开music_test.py,先让他运行着。

2.2 学习原理

2.2.1 TCN网络结构直观了解(参考:机器学习进阶之 时域/时间卷积网络 TCN 概念+由来+原理+代码实现

这部分内容对应tcn.py中的class Chomp1dclass TemporalBlock
在这里插入图片描述
TCN网络结构左边一大串主要包括四个部分:
膨胀因果卷积(Dilated Causal Conv膨胀就是说卷积时的输入存在间隔采样;因果指每层某时刻的数据只依赖于之前层当前时刻及之前时刻的数据,与未来时刻的数据无关;卷积就是CNN的卷积(卷积核在数据上进行的一种滑动运算的操作)。
权重归一化(WeightNorm:通过重写深度网络的权重来进行加速。代码tcn.py中从torch.nn.utils中调用weight_norm使用。
激活函数(ReLU:挺有名的,从torch.nn中调用。
Dropout:指在深度学习网络的训练过程中,对于神经网络单元,按照一定的概率将其暂时从网络中丢弃。意义是防止过拟合,提高模型的运算速度。
TCN网络结构右边是残差连接:
残差连接
1*1的卷积块儿,作者说:不仅可以使网络拥有跨层传递信息的功能,而且可以保证输入输出的一致性。

2.2.2 TCN结构关系详解(参考:时间卷积网络(TCN):结构+pytorch代码,有对代码非常详细的标注)

TCN与LSTM的区别:LSTM是通过引入卷积操作使其能够处理图像信息,卷积只对一个时刻的输入图像进行操作;而TCN是利用卷积进行跨时间步提取特征。
TCN的实现——1-D FCN结构;
TCN的实现——因果卷积、膨胀因果卷积(对比膨胀非因果卷积)、残差块结构(参考ResNet,使TCN结构更具有泛化能力)
在这里插入图片描述

2.3测试结果

Namespace(clip=0.2, cuda=True, data='Nott', dropout=0.25, epochs=100, ksize=5, levels=4, log_interval=100, lr=0.001, nhid=150, optim='Adam', seed=1111)
loading Nott data...
Epoch  1 | lr 0.00100 | loss 24.20483
Epoch  1 | lr 0.00100 | loss 12.54757
Epoch  1 | lr 0.00100 | loss 10.34167
Epoch  1 | lr 0.00100 | loss 7.46519
Epoch  1 | lr 0.00100 | loss 6.22717
Epoch  1 | lr 0.00100 | loss 5.83443
Validation loss: 5.29395
Test loss: 5.40475
Saved model!

Epoch  2 | lr 0.00100 | loss 5.49445
Epoch  2 | lr 0.00100 | loss 5.08582
Epoch  2 | lr 0.00100 | loss 5.28078
Epoch  2 | lr 0.00100 | loss 5.21557
Epoch  2 | lr 0.00100 | loss 5.09972
Epoch  2 | lr 0.00100 | loss 4.87487
Validation loss: 4.88671
Test loss: 4.91229
Saved model!

Epoch  3 | lr 0.00100 | loss 4.55071
Epoch  3 | lr 0.00100 | loss 4.64663
Epoch  3 | lr 0.00100 | loss 4.62720
Epoch  3 | lr 0.00100 | loss 4.40581
Epoch  3 | lr 0.00100 | loss 4.54712
Epoch  3 | lr 0.00100 | loss 4.48989
Validation loss: 4.23855
Test loss: 4.27290
Saved model!

Epoch  4 | lr 0.00100 | loss 4.15868
Epoch  4 | lr 0.00100 | loss 4.19424
Epoch  4 | lr 0.00100 | loss 3.93361
Epoch  4 | lr 0.00100 | loss 3.87698
Epoch  4 | lr 0.00100 | loss 4.26776
Epoch  4 | lr 0.00100 | loss 4.32880
Validation loss: 4.00616
Test loss: 4.04496
Saved model!

Epoch  5 | lr 0.00100 | loss 4.02574
Epoch  5 | lr 0.00100 | loss 4.59837
Epoch  5 | lr 0.00100 | loss 4.17430
Epoch  5 | lr 0.00100 | loss 3.96050
Epoch  5 | lr 0.00100 | loss 4.04181
Epoch  5 | lr 0.00100 | loss 3.97466
Validation loss: 3.78924
Test loss: 3.84233
Saved model!

Epoch  6 | lr 0.00100 | loss 3.77337
Epoch  6 | lr 0.00100 | loss 3.78759
Epoch  6 | lr 0.00100 | loss 4.05782
Epoch  6 | lr 0.00100 | loss 3.61807
Epoch  6 | lr 0.00100 | loss 3.66880
Epoch  6 | lr 0.00100 | loss 3.68237
Validation loss: 3.69415
Test loss: 3.71941
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Epoch  7 | lr 0.00100 | loss 3.71184
Epoch  7 | lr 0.00100 | loss 3.65575
Epoch  7 | lr 0.00100 | loss 3.50422
Epoch  7 | lr 0.00100 | loss 3.69709
Epoch  7 | lr 0.00100 | loss 3.39189
Epoch  7 | lr 0.00100 | loss 3.60912
Validation loss: 3.50421
Test loss: 3.52113
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Epoch  8 | lr 0.00100 | loss 3.39342
Epoch  8 | lr 0.00100 | loss 3.45223
Epoch  8 | lr 0.00100 | loss 3.47272
Epoch  8 | lr 0.00100 | loss 3.47585
Epoch  8 | lr 0.00100 | loss 3.88333
Epoch  8 | lr 0.00100 | loss 3.51368
Validation loss: 3.45557
Test loss: 3.46655
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Epoch  9 | lr 0.00100 | loss 3.38787
Epoch  9 | lr 0.00100 | loss 3.49427
Epoch  9 | lr 0.00100 | loss 3.42003
Epoch  9 | lr 0.00100 | loss 3.45465
Epoch  9 | lr 0.00100 | loss 3.44894
Epoch  9 | lr 0.00100 | loss 3.35138
Validation loss: 3.39177
Test loss: 3.39885
Saved model!

Epoch 10 | lr 0.00100 | loss 3.33982
Epoch 10 | lr 0.00100 | loss 3.33333
Epoch 10 | lr 0.00100 | loss 3.27813
Epoch 10 | lr 0.00100 | loss 3.39872
Epoch 10 | lr 0.00100 | loss 3.31045
Epoch 10 | lr 0.00100 | loss 3.47179
Validation loss: 3.35350
Test loss: 3.35821
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Epoch 11 | lr 0.00100 | loss 3.24939
Epoch 11 | lr 0.00100 | loss 3.28225
Epoch 11 | lr 0.00100 | loss 3.31755
Epoch 11 | lr 0.00100 | loss 3.31538
Epoch 11 | lr 0.00100 | loss 3.34717
Epoch 11 | lr 0.00100 | loss 3.47794
Validation loss: 3.27830
Test loss: 3.28621
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Epoch 12 | lr 0.00100 | loss 3.24459
Epoch 12 | lr 0.00100 | loss 3.26871
Epoch 12 | lr 0.00100 | loss 2.83995
Epoch 12 | lr 0.00100 | loss 3.24781
Epoch 12 | lr 0.00100 | loss 3.25777
Epoch 12 | lr 0.00100 | loss 3.09675
Validation loss: 3.25199
Test loss: 3.25987
Saved model!

Epoch 13 | lr 0.00100 | loss 3.18712
Epoch 13 | lr 0.00100 | loss 3.15744
Epoch 13 | lr 0.00100 | loss 3.08412
Epoch 13 | lr 0.00100 | loss 2.98677
Epoch 13 | lr 0.00100 | loss 3.23000
Epoch 13 | lr 0.00100 | loss 3.12484
Validation loss: 3.22609
Test loss: 3.22669
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Epoch 14 | lr 0.00100 | loss 2.86843
Epoch 14 | lr 0.00100 | loss 3.05798
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Epoch 14 | lr 0.00100 | loss 3.14372
Epoch 14 | lr 0.00100 | loss 3.19728
Epoch 14 | lr 0.00100 | loss 3.12642
Validation loss: 3.20776
Test loss: 3.20785
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Epoch 15 | lr 0.00100 | loss 3.09529
Epoch 15 | lr 0.00100 | loss 3.05085
Epoch 15 | lr 0.00100 | loss 3.12605
Epoch 15 | lr 0.00100 | loss 3.14538
Epoch 15 | lr 0.00100 | loss 3.09047
Epoch 15 | lr 0.00100 | loss 3.14403
Validation loss: 3.19157
Test loss: 3.19761
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Epoch 16 | lr 0.00100 | loss 3.08435
Epoch 16 | lr 0.00100 | loss 3.06446
Epoch 16 | lr 0.00100 | loss 3.07964
Epoch 16 | lr 0.00100 | loss 2.92217
Epoch 16 | lr 0.00100 | loss 3.02095
Epoch 16 | lr 0.00100 | loss 3.04373
Validation loss: 3.18486
Test loss: 3.18550
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Epoch 17 | lr 0.00100 | loss 3.02295
Epoch 17 | lr 0.00100 | loss 2.94601
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Epoch 17 | lr 0.00100 | loss 3.02466
Epoch 17 | lr 0.00100 | loss 2.96160
Epoch 17 | lr 0.00100 | loss 3.63558
Validation loss: 3.14967
Test loss: 3.15910
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Epoch 18 | lr 0.00100 | loss 3.01251
Epoch 18 | lr 0.00100 | loss 2.82075
Epoch 18 | lr 0.00100 | loss 2.78892
Epoch 18 | lr 0.00100 | loss 2.99531
Epoch 18 | lr 0.00100 | loss 2.96843
Epoch 18 | lr 0.00100 | loss 2.98169
Validation loss: 3.14602
Test loss: 3.15058
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Epoch 19 | lr 0.00100 | loss 2.90797
Epoch 19 | lr 0.00100 | loss 3.09173
Epoch 19 | lr 0.00100 | loss 2.91924
Epoch 19 | lr 0.00100 | loss 2.99306
Epoch 19 | lr 0.00100 | loss 2.91742
Epoch 19 | lr 0.00100 | loss 2.93122
Validation loss: 3.13545
Test loss: 3.13629
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Epoch 20 | lr 0.00100 | loss 2.81639
Epoch 20 | lr 0.00100 | loss 2.90578
Epoch 20 | lr 0.00100 | loss 2.88055
Epoch 20 | lr 0.00100 | loss 2.93285
Epoch 20 | lr 0.00100 | loss 3.00227
Epoch 20 | lr 0.00100 | loss 1.93661
Validation loss: 3.12148
Test loss: 3.11480
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Epoch 21 | lr 0.00100 | loss 2.72758
Epoch 21 | lr 0.00100 | loss 2.84461
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Epoch 21 | lr 0.00100 | loss 2.96725
Epoch 21 | lr 0.00100 | loss 2.87752
Epoch 21 | lr 0.00100 | loss 2.14672
Validation loss: 3.08553
Test loss: 3.09944
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Epoch 22 | lr 0.00100 | loss 2.81496
Epoch 22 | lr 0.00100 | loss 2.86394
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Epoch 22 | lr 0.00100 | loss 2.87718
Epoch 22 | lr 0.00100 | loss 2.79423
Epoch 22 | lr 0.00100 | loss 2.84248
Validation loss: 3.07362
Test loss: 3.07531
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Epoch 23 | lr 0.00100 | loss 2.80338
Epoch 23 | lr 0.00100 | loss 2.77892
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Epoch 23 | lr 0.00100 | loss 2.80235
Epoch 23 | lr 0.00100 | loss 2.89891
Epoch 23 | lr 0.00100 | loss 2.83766
Validation loss: 3.07538
Test loss: 3.07808
Epoch 24 | lr 0.00100 | loss 2.69057
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Epoch 24 | lr 0.00100 | loss 2.96076
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Epoch 24 | lr 0.00100 | loss 2.76815
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Validation loss: 3.05619
Test loss: 3.05848
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Epoch 25 | lr 0.00100 | loss 2.58305
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Validation loss: 3.04583
Test loss: 3.05974
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Epoch 26 | lr 0.00100 | loss 2.67008
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Validation loss: 3.02619
Test loss: 3.03652
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Epoch 27 | lr 0.00100 | loss 2.59768
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Epoch 27 | lr 0.00100 | loss 2.73795
Validation loss: 3.00045
Test loss: 3.01429
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Epoch 28 | lr 0.00100 | loss 2.62839
Epoch 28 | lr 0.00100 | loss 2.54048
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Epoch 28 | lr 0.00100 | loss 2.59507
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Validation loss: 3.00037
Test loss: 3.00544
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Epoch 29 | lr 0.00100 | loss 2.64653
Epoch 29 | lr 0.00100 | loss 2.58176
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Epoch 29 | lr 0.00100 | loss 2.80495
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Validation loss: 3.00765
Test loss: 3.01136
Epoch 30 | lr 0.00100 | loss 2.69717
Epoch 30 | lr 0.00100 | loss 2.54373
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Epoch 30 | lr 0.00100 | loss 2.58480
Epoch 30 | lr 0.00100 | loss 2.59596
Epoch 30 | lr 0.00100 | loss 2.69300
Validation loss: 3.01752
Test loss: 3.01258
Epoch 31 | lr 0.00010 | loss 2.45645
Epoch 31 | lr 0.00010 | loss 2.45380
Epoch 31 | lr 0.00010 | loss 2.48504
Epoch 31 | lr 0.00010 | loss 2.51676
Epoch 31 | lr 0.00010 | loss 2.56140
Epoch 31 | lr 0.00010 | loss 2.45933
Validation loss: 2.95486
Test loss: 2.96315
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Epoch 32 | lr 0.00010 | loss 2.43954
Epoch 32 | lr 0.00010 | loss 2.43467
Epoch 32 | lr 0.00010 | loss 2.42177
Epoch 32 | lr 0.00010 | loss 2.46623
Epoch 32 | lr 0.00010 | loss 2.61942
Epoch 32 | lr 0.00010 | loss 2.46129
Validation loss: 2.95515
Test loss: 2.96563
Epoch 33 | lr 0.00010 | loss 2.54713
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Epoch 33 | lr 0.00010 | loss 2.34418
Epoch 33 | lr 0.00010 | loss 2.44249
Epoch 33 | lr 0.00010 | loss 2.53604
Epoch 33 | lr 0.00010 | loss 2.43318
Validation loss: 2.95291
Test loss: 2.96509
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Epoch 34 | lr 0.00010 | loss 2.43941
Epoch 34 | lr 0.00010 | loss 2.41067
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Epoch 34 | lr 0.00010 | loss 2.62946
Epoch 34 | lr 0.00010 | loss 2.46241
Epoch 34 | lr 0.00010 | loss 2.36850
Validation loss: 2.95889
Test loss: 2.96941
Epoch 35 | lr 0.00001 | loss 2.43545
Epoch 35 | lr 0.00001 | loss 2.44627
Epoch 35 | lr 0.00001 | loss 3.08806
Epoch 35 | lr 0.00001 | loss 2.42842
Epoch 35 | lr 0.00001 | loss 2.24893
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Validation loss: 2.95521
Test loss: 2.96670
Epoch 36 | lr 0.00001 | loss 2.34449
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Validation loss: 2.95483
Test loss: 2.96588
Epoch 37 | lr 0.00001 | loss 2.43688
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Validation loss: 2.95496
Test loss: 2.96567
Epoch 38 | lr 0.00001 | loss 2.34746
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Epoch 38 | lr 0.00001 | loss 2.41640
Epoch 38 | lr 0.00001 | loss 2.15776
Validation loss: 2.95320
Test loss: 2.96515
Epoch 39 | lr 0.00001 | loss 2.40601
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Epoch 39 | lr 0.00001 | loss 2.53223
Epoch 39 | lr 0.00001 | loss 2.00882
Epoch 39 | lr 0.00001 | loss 2.34943
Epoch 39 | lr 0.00001 | loss 2.43459
Validation loss: 2.95460
Test loss: 2.96632
Epoch 40 | lr 0.00001 | loss 2.48286
Epoch 40 | lr 0.00001 | loss 2.33617
Epoch 40 | lr 0.00001 | loss 2.42163
Epoch 40 | lr 0.00001 | loss 2.35010
Epoch 40 | lr 0.00001 | loss 2.40796
Epoch 40 | lr 0.00001 | loss 2.45041
Validation loss: 2.95403
Test loss: 2.96556
Epoch 41 | lr 0.00001 | loss 2.40313
Epoch 41 | lr 0.00001 | loss 2.32656
Epoch 41 | lr 0.00001 | loss 2.47946
Epoch 41 | lr 0.00001 | loss 2.15760
Epoch 41 | lr 0.00001 | loss 2.37480
Epoch 41 | lr 0.00001 | loss 2.46791
Validation loss: 2.95404
Test loss: 2.96532
Epoch 42 | lr 0.00001 | loss 2.45571
Epoch 42 | lr 0.00001 | loss 2.39349
Epoch 42 | lr 0.00001 | loss 2.40195
Epoch 42 | lr 0.00001 | loss 2.40755
Epoch 42 | lr 0.00001 | loss 2.20085
Epoch 42 | lr 0.00001 | loss 2.55087
Validation loss: 2.95563
Test loss: 2.96605
Epoch 43 | lr 0.00000 | loss 2.41390
Epoch 43 | lr 0.00000 | loss 2.38766
Epoch 43 | lr 0.00000 | loss 2.40005
Epoch 43 | lr 0.00000 | loss 2.40574
Epoch 43 | lr 0.00000 | loss 2.45363
Epoch 43 | lr 0.00000 | loss 2.45474
Validation loss: 2.95526
Test loss: 2.96588
Epoch 44 | lr 0.00000 | loss 2.44101
Epoch 44 | lr 0.00000 | loss 2.38717
Epoch 44 | lr 0.00000 | loss 2.42643
Epoch 44 | lr 0.00000 | loss 2.37804
Epoch 44 | lr 0.00000 | loss 2.40502
Epoch 44 | lr 0.00000 | loss 2.44630
Validation loss: 2.95480
Test loss: 2.96562
Epoch 45 | lr 0.00000 | loss 2.35229
Epoch 45 | lr 0.00000 | loss 2.39950
Epoch 45 | lr 0.00000 | loss 2.47582
Epoch 45 | lr 0.00000 | loss 2.46909
Epoch 45 | lr 0.00000 | loss 2.40886
Epoch 45 | lr 0.00000 | loss 2.46704
Validation loss: 2.95471
Test loss: 2.96563
Epoch 46 | lr 0.00000 | loss 2.46100
Epoch 46 | lr 0.00000 | loss 1.39584
Epoch 46 | lr 0.00000 | loss 2.35312
Epoch 46 | lr 0.00000 | loss 2.70966
Epoch 46 | lr 0.00000 | loss 2.71677
Epoch 46 | lr 0.00000 | loss 2.42208
Validation loss: 2.95453
Test loss: 2.96552
Epoch 47 | lr 0.00000 | loss 2.43515
Epoch 47 | lr 0.00000 | loss 2.50489
Epoch 47 | lr 0.00000 | loss 2.41215
Epoch 47 | lr 0.00000 | loss 2.34724
Epoch 47 | lr 0.00000 | loss 2.49304
Epoch 47 | lr 0.00000 | loss 2.32401
Validation loss: 2.95436
Test loss: 2.96538
Epoch 48 | lr 0.00000 | loss 2.41615
Epoch 48 | lr 0.00000 | loss 2.39621
Epoch 48 | lr 0.00000 | loss 2.38097
Epoch 48 | lr 0.00000 | loss 2.44820
Epoch 48 | lr 0.00000 | loss 2.02717
Epoch 48 | lr 0.00000 | loss 2.44434
Validation loss: 2.95430
Test loss: 2.96533
Epoch 49 | lr 0.00000 | loss 2.39831
Epoch 49 | lr 0.00000 | loss 2.53042
Epoch 49 | lr 0.00000 | loss 2.48773
Epoch 49 | lr 0.00000 | loss 2.45923
Epoch 49 | lr 0.00000 | loss 2.39248
Epoch 49 | lr 0.00000 | loss 2.41314
Validation loss: 2.95415
Test loss: 2.96527
Epoch 50 | lr 0.00000 | loss 2.34241
Epoch 50 | lr 0.00000 | loss 2.43070
Epoch 50 | lr 0.00000 | loss 2.05006
Epoch 50 | lr 0.00000 | loss 2.49058
Epoch 50 | lr 0.00000 | loss 2.40379
Epoch 50 | lr 0.00000 | loss 2.46354
Validation loss: 2.95412
Test loss: 2.96525
Epoch 51 | lr 0.00000 | loss 2.50044
Epoch 51 | lr 0.00000 | loss 2.31235
Epoch 51 | lr 0.00000 | loss 2.35816
Epoch 51 | lr 0.00000 | loss 2.48627
Epoch 51 | lr 0.00000 | loss 2.42042
Epoch 51 | lr 0.00000 | loss 2.40909
Validation loss: 2.95393
Test loss: 2.96513
Epoch 52 | lr 0.00000 | loss 2.41315
Epoch 52 | lr 0.00000 | loss 2.44901
Epoch 52 | lr 0.00000 | loss 1.71025
Epoch 52 | lr 0.00000 | loss 2.42413
Epoch 52 | lr 0.00000 | loss 2.42102
Epoch 52 | lr 0.00000 | loss 2.39134
Validation loss: 2.95397
Test loss: 2.96515
Epoch 53 | lr 0.00000 | loss 2.40649
Epoch 53 | lr 0.00000 | loss 2.54095
Epoch 53 | lr 0.00000 | loss 2.19728
Epoch 53 | lr 0.00000 | loss 2.51835
Epoch 53 | lr 0.00000 | loss 2.40190
Epoch 53 | lr 0.00000 | loss 2.39805
Validation loss: 2.95385
Test loss: 2.96504
Epoch 54 | lr 0.00000 | loss 2.39350
Epoch 54 | lr 0.00000 | loss 2.49204
Epoch 54 | lr 0.00000 | loss 2.31756
Epoch 54 | lr 0.00000 | loss 2.43664
Epoch 54 | lr 0.00000 | loss 2.39233
Epoch 54 | lr 0.00000 | loss 2.46368
Validation loss: 2.95395
Test loss: 2.96514
Epoch 55 | lr 0.00000 | loss 2.39194
Epoch 55 | lr 0.00000 | loss 2.46516
Epoch 55 | lr 0.00000 | loss 2.45878
Epoch 55 | lr 0.00000 | loss 2.35791
Epoch 55 | lr 0.00000 | loss 2.23562
Epoch 55 | lr 0.00000 | loss 2.40309
Validation loss: 2.95402
Test loss: 2.96521
Epoch 56 | lr 0.00000 | loss 2.42875
Epoch 56 | lr 0.00000 | loss 2.39907
Epoch 56 | lr 0.00000 | loss 2.35058
Epoch 56 | lr 0.00000 | loss 2.46811
Epoch 56 | lr 0.00000 | loss 2.37041
Epoch 56 | lr 0.00000 | loss 2.40081
Validation loss: 2.95403
Test loss: 2.96521
Epoch 57 | lr 0.00000 | loss 2.42965
Epoch 57 | lr 0.00000 | loss 2.36886
Epoch 57 | lr 0.00000 | loss 2.52495
Epoch 57 | lr 0.00000 | loss 2.40957
Epoch 57 | lr 0.00000 | loss 2.50273
Epoch 57 | lr 0.00000 | loss 2.31355
Validation loss: 2.95403
Test loss: 2.96521
Epoch 58 | lr 0.00000 | loss 2.44439
Epoch 58 | lr 0.00000 | loss 2.44985
Epoch 58 | lr 0.00000 | loss 2.35233
Epoch 58 | lr 0.00000 | loss 2.40324
Epoch 58 | lr 0.00000 | loss 2.44942
Epoch 58 | lr 0.00000 | loss 2.45389
Validation loss: 2.95402
Test loss: 2.96521
Epoch 59 | lr 0.00000 | loss 2.38148
Epoch 59 | lr 0.00000 | loss 2.36841
Epoch 59 | lr 0.00000 | loss 2.41448
Epoch 59 | lr 0.00000 | loss 2.44373
Epoch 59 | lr 0.00000 | loss 2.44111
Epoch 59 | lr 0.00000 | loss 2.45866
Validation loss: 2.95402
Test loss: 2.96520
Epoch 60 | lr 0.00000 | loss 2.41296
Epoch 60 | lr 0.00000 | loss 2.53527
Epoch 60 | lr 0.00000 | loss 2.39205
Epoch 60 | lr 0.00000 | loss 2.31394
Epoch 60 | lr 0.00000 | loss 2.38146
Epoch 60 | lr 0.00000 | loss 2.43245
Validation loss: 2.95402
Test loss: 2.96520
Epoch 61 | lr 0.00000 | loss 2.48459
Epoch 61 | lr 0.00000 | loss 2.36444
Epoch 61 | lr 0.00000 | loss 2.42401
Epoch 61 | lr 0.00000 | loss 2.38782
Epoch 61 | lr 0.00000 | loss 2.39042
Epoch 61 | lr 0.00000 | loss 2.40236
Validation loss: 2.95402
Test loss: 2.96520
Epoch 62 | lr 0.00000 | loss 2.43595
Epoch 62 | lr 0.00000 | loss 2.44351
Epoch 62 | lr 0.00000 | loss 2.38162
Epoch 62 | lr 0.00000 | loss 2.41288
Epoch 62 | lr 0.00000 | loss 2.44867
Epoch 62 | lr 0.00000 | loss 2.20912
Validation loss: 2.95402
Test loss: 2.96520
Epoch 63 | lr 0.00000 | loss 2.18615
Epoch 63 | lr 0.00000 | loss 2.54030
Epoch 63 | lr 0.00000 | loss 2.47183
Epoch 63 | lr 0.00000 | loss 2.39264
Epoch 63 | lr 0.00000 | loss 2.38341
Epoch 63 | lr 0.00000 | loss 2.43780
Validation loss: 2.95402
Test loss: 2.96520
Epoch 64 | lr 0.00000 | loss 2.44530
Epoch 64 | lr 0.00000 | loss 2.28641
Epoch 64 | lr 0.00000 | loss 2.26978
Epoch 64 | lr 0.00000 | loss 2.47008
Epoch 64 | lr 0.00000 | loss 2.46534
Epoch 64 | lr 0.00000 | loss 2.40426
Validation loss: 2.95401
Test loss: 2.96520
Epoch 65 | lr 0.00000 | loss 2.45915
Epoch 65 | lr 0.00000 | loss 2.50910
Epoch 65 | lr 0.00000 | loss 2.48938
Epoch 65 | lr 0.00000 | loss 2.32067
Epoch 65 | lr 0.00000 | loss 2.37479
Epoch 65 | lr 0.00000 | loss 2.51838
Validation loss: 2.95401
Test loss: 2.96520
Epoch 66 | lr 0.00000 | loss 2.43692
Epoch 66 | lr 0.00000 | loss 2.34911
Epoch 66 | lr 0.00000 | loss 2.30305
Epoch 66 | lr 0.00000 | loss 2.37067
Epoch 66 | lr 0.00000 | loss 2.40642
Epoch 66 | lr 0.00000 | loss 2.46048
Validation loss: 2.95401
Test loss: 2.96520
Epoch 67 | lr 0.00000 | loss 2.59787
Epoch 67 | lr 0.00000 | loss 2.47146
Epoch 67 | lr 0.00000 | loss 2.43156
Epoch 67 | lr 0.00000 | loss 2.44966
Epoch 67 | lr 0.00000 | loss 2.40391
Epoch 67 | lr 0.00000 | loss 2.37677
Validation loss: 2.95401
Test loss: 2.96520
Epoch 68 | lr 0.00000 | loss 2.41856
Epoch 68 | lr 0.00000 | loss 2.47008
Epoch 68 | lr 0.00000 | loss 2.47840
Epoch 68 | lr 0.00000 | loss 2.36878
Epoch 68 | lr 0.00000 | loss 2.43735
Epoch 68 | lr 0.00000 | loss 2.34884
Validation loss: 2.95401
Test loss: 2.96519
Epoch 69 | lr 0.00000 | loss 1.76942
Epoch 69 | lr 0.00000 | loss 2.38943
Epoch 69 | lr 0.00000 | loss 2.41059
Epoch 69 | lr 0.00000 | loss 2.41351
Epoch 69 | lr 0.00000 | loss 2.48355
Epoch 69 | lr 0.00000 | loss 2.46324
Validation loss: 2.95401
Test loss: 2.96520
Epoch 70 | lr 0.00000 | loss 2.08691
Epoch 70 | lr 0.00000 | loss 2.44040
Epoch 70 | lr 0.00000 | loss 2.36904
Epoch 70 | lr 0.00000 | loss 2.42060
Epoch 70 | lr 0.00000 | loss 2.43333
Epoch 70 | lr 0.00000 | loss 2.41498
Validation loss: 2.95401
Test loss: 2.96520
Epoch 71 | lr 0.00000 | loss 2.26960
Epoch 71 | lr 0.00000 | loss 2.28289
Epoch 71 | lr 0.00000 | loss 2.36861
Epoch 71 | lr 0.00000 | loss 2.38697
Epoch 71 | lr 0.00000 | loss 2.47841
Epoch 71 | lr 0.00000 | loss 2.48060
Validation loss: 2.95401
Test loss: 2.96520
Epoch 72 | lr 0.00000 | loss 2.13208
Epoch 72 | lr 0.00000 | loss 2.41577
Epoch 72 | lr 0.00000 | loss 2.42331
Epoch 72 | lr 0.00000 | loss 2.48011
Epoch 72 | lr 0.00000 | loss 1.39558
Epoch 72 | lr 0.00000 | loss 2.46180
Validation loss: 2.95401
Test loss: 2.96520
Epoch 73 | lr 0.00000 | loss 2.39402
Epoch 73 | lr 0.00000 | loss 2.48592
Epoch 73 | lr 0.00000 | loss 2.36022
Epoch 73 | lr 0.00000 | loss 2.47524
Epoch 73 | lr 0.00000 | loss 2.13461
Epoch 73 | lr 0.00000 | loss 2.36569
Validation loss: 2.95401
Test loss: 2.96520
Epoch 74 | lr 0.00000 | loss 2.38321
Epoch 74 | lr 0.00000 | loss 2.44158
Epoch 74 | lr 0.00000 | loss 2.26542
Epoch 74 | lr 0.00000 | loss 2.35360
Epoch 74 | lr 0.00000 | loss 2.44588
Epoch 74 | lr 0.00000 | loss 2.41055
Validation loss: 2.95401
Test loss: 2.96520
Epoch 75 | lr 0.00000 | loss 2.44660
Epoch 75 | lr 0.00000 | loss 2.47491
Epoch 75 | lr 0.00000 | loss 2.42964
Epoch 75 | lr 0.00000 | loss 2.41180
Epoch 75 | lr 0.00000 | loss 2.44037
Epoch 75 | lr 0.00000 | loss 2.39054
Validation loss: 2.95401
Test loss: 2.96520
Epoch 76 | lr 0.00000 | loss 2.42163
Epoch 76 | lr 0.00000 | loss 2.47723
Epoch 76 | lr 0.00000 | loss 2.46514
Epoch 76 | lr 0.00000 | loss 2.34455
Epoch 76 | lr 0.00000 | loss 2.40418
Epoch 76 | lr 0.00000 | loss 2.40259
Validation loss: 2.95401
Test loss: 2.96519
Epoch 77 | lr 0.00000 | loss 2.41411
Epoch 77 | lr 0.00000 | loss 2.45589
Epoch 77 | lr 0.00000 | loss 2.44414
Epoch 77 | lr 0.00000 | loss 2.37484
Epoch 77 | lr 0.00000 | loss 2.37498
Epoch 77 | lr 0.00000 | loss 2.31428
Validation loss: 2.95401
Test loss: 2.96519
Epoch 78 | lr 0.00000 | loss 2.55251
Epoch 78 | lr 0.00000 | loss 2.31894
Epoch 78 | lr 0.00000 | loss 2.44500
Epoch 78 | lr 0.00000 | loss 2.42809
Epoch 78 | lr 0.00000 | loss 2.46257
Epoch 78 | lr 0.00000 | loss 2.40419
Validation loss: 2.95401
Test loss: 2.96519
Epoch 79 | lr 0.00000 | loss 2.32429
Epoch 79 | lr 0.00000 | loss 2.53482
Epoch 79 | lr 0.00000 | loss 2.42113
Epoch 79 | lr 0.00000 | loss 2.17599
Epoch 79 | lr 0.00000 | loss 2.41099
Epoch 79 | lr 0.00000 | loss 2.59278
Validation loss: 2.95400
Test loss: 2.96519
Epoch 80 | lr 0.00000 | loss 2.39924
Epoch 80 | lr 0.00000 | loss 2.65279
Epoch 80 | lr 0.00000 | loss 2.44098
Epoch 80 | lr 0.00000 | loss 2.36354
Epoch 80 | lr 0.00000 | loss 2.25048
Epoch 80 | lr 0.00000 | loss 2.35756
Validation loss: 2.95400
Test loss: 2.96519
Epoch 81 | lr 0.00000 | loss 2.41862
Epoch 81 | lr 0.00000 | loss 2.48602
Epoch 81 | lr 0.00000 | loss 2.48530
Epoch 81 | lr 0.00000 | loss 2.66520
Epoch 81 | lr 0.00000 | loss 2.43285
Epoch 81 | lr 0.00000 | loss 2.35819
Validation loss: 2.95400
Test loss: 2.96519
Epoch 82 | lr 0.00000 | loss 2.42112
Epoch 82 | lr 0.00000 | loss 2.32117
Epoch 82 | lr 0.00000 | loss 2.36124
Epoch 82 | lr 0.00000 | loss 2.36869
Epoch 82 | lr 0.00000 | loss 2.56043
Epoch 82 | lr 0.00000 | loss 2.40713
Validation loss: 2.95400
Test loss: 2.96520
Epoch 83 | lr 0.00000 | loss 2.77187
Epoch 83 | lr 0.00000 | loss 2.41533
Epoch 83 | lr 0.00000 | loss 2.36156
Epoch 83 | lr 0.00000 | loss 2.52006
Epoch 83 | lr 0.00000 | loss 2.44264
Epoch 83 | lr 0.00000 | loss 2.48203
Validation loss: 2.95400
Test loss: 2.96519
Epoch 84 | lr 0.00000 | loss 2.39321
Epoch 84 | lr 0.00000 | loss 1.88318
Epoch 84 | lr 0.00000 | loss 2.40187
Epoch 84 | lr 0.00000 | loss 2.43431
Epoch 84 | lr 0.00000 | loss 2.57168
Epoch 84 | lr 0.00000 | loss 2.33964
Validation loss: 2.95400
Test loss: 2.96519
Epoch 85 | lr 0.00000 | loss 2.40599
Epoch 85 | lr 0.00000 | loss 2.42410
Epoch 85 | lr 0.00000 | loss 2.39999
Epoch 85 | lr 0.00000 | loss 2.47565
Epoch 85 | lr 0.00000 | loss 2.37174
Epoch 85 | lr 0.00000 | loss 2.45941
Validation loss: 2.95400
Test loss: 2.96519
Epoch 86 | lr 0.00000 | loss 2.15863
Epoch 86 | lr 0.00000 | loss 2.37759
Epoch 86 | lr 0.00000 | loss 2.56286
Epoch 86 | lr 0.00000 | loss 2.42264
Epoch 86 | lr 0.00000 | loss 2.47878
Epoch 86 | lr 0.00000 | loss 2.46373
Validation loss: 2.95400
Test loss: 2.96519
Epoch 87 | lr 0.00000 | loss 2.76105
Epoch 87 | lr 0.00000 | loss 2.35281
Epoch 87 | lr 0.00000 | loss 2.45527
Epoch 87 | lr 0.00000 | loss 2.45856
Epoch 87 | lr 0.00000 | loss 2.62649
Epoch 87 | lr 0.00000 | loss 2.52481
Validation loss: 2.95400
Test loss: 2.96519
Epoch 88 | lr 0.00000 | loss 2.47774
Epoch 88 | lr 0.00000 | loss 2.34679
Epoch 88 | lr 0.00000 | loss 2.44432
Epoch 88 | lr 0.00000 | loss 2.12840
Epoch 88 | lr 0.00000 | loss 2.51886
Epoch 88 | lr 0.00000 | loss 2.06461
Validation loss: 2.95400
Test loss: 2.96519
Epoch 89 | lr 0.00000 | loss 2.37020
Epoch 89 | lr 0.00000 | loss 2.47868
Epoch 89 | lr 0.00000 | loss 2.39565
Epoch 89 | lr 0.00000 | loss 2.40516
Epoch 89 | lr 0.00000 | loss 2.41972
Epoch 89 | lr 0.00000 | loss 2.38832
Validation loss: 2.95400
Test loss: 2.96519
Epoch 90 | lr 0.00000 | loss 2.23446
Epoch 90 | lr 0.00000 | loss 2.45653
Epoch 90 | lr 0.00000 | loss 2.40566
Epoch 90 | lr 0.00000 | loss 2.49196
Epoch 90 | lr 0.00000 | loss 2.36378
Epoch 90 | lr 0.00000 | loss 2.41977
Validation loss: 2.95400
Test loss: 2.96519
Epoch 91 | lr 0.00000 | loss 2.34804
Epoch 91 | lr 0.00000 | loss 2.42081
Epoch 91 | lr 0.00000 | loss 2.42765
Epoch 91 | lr 0.00000 | loss 2.51739
Epoch 91 | lr 0.00000 | loss 2.50900
Epoch 91 | lr 0.00000 | loss 2.50998
Validation loss: 2.95400
Test loss: 2.96519
Epoch 92 | lr 0.00000 | loss 2.44960
Epoch 92 | lr 0.00000 | loss 2.38403
Epoch 92 | lr 0.00000 | loss 2.49420
Epoch 92 | lr 0.00000 | loss 2.32383
Epoch 92 | lr 0.00000 | loss 2.22930
Epoch 92 | lr 0.00000 | loss 2.41387
Validation loss: 2.95400
Test loss: 2.96519
Epoch 93 | lr 0.00000 | loss 2.50621
Epoch 93 | lr 0.00000 | loss 2.40276
Epoch 93 | lr 0.00000 | loss 2.35815
Epoch 93 | lr 0.00000 | loss 2.42412
Epoch 93 | lr 0.00000 | loss 2.36929
Epoch 93 | lr 0.00000 | loss 2.40508
Validation loss: 2.95400
Test loss: 2.96519
Epoch 94 | lr 0.00000 | loss 2.32516
Epoch 94 | lr 0.00000 | loss 2.63810
Epoch 94 | lr 0.00000 | loss 2.53540
Epoch 94 | lr 0.00000 | loss 2.49643
Epoch 94 | lr 0.00000 | loss 2.43261
Epoch 94 | lr 0.00000 | loss 2.39358
Validation loss: 2.95400
Test loss: 2.96519
Epoch 95 | lr 0.00000 | loss 2.37413
Epoch 95 | lr 0.00000 | loss 2.41371
Epoch 95 | lr 0.00000 | loss 1.82993
Epoch 95 | lr 0.00000 | loss 2.46905
Epoch 95 | lr 0.00000 | loss 2.41483
Epoch 95 | lr 0.00000 | loss 2.42171
Validation loss: 2.95400
Test loss: 2.96519
Epoch 96 | lr 0.00000 | loss 2.40594
Epoch 96 | lr 0.00000 | loss 2.46985
Epoch 96 | lr 0.00000 | loss 2.41713
Epoch 96 | lr 0.00000 | loss 2.42794
Epoch 96 | lr 0.00000 | loss 2.34145
Epoch 96 | lr 0.00000 | loss 2.39331
Validation loss: 2.95400
Test loss: 2.96519
Epoch 97 | lr 0.00000 | loss 2.46766
Epoch 97 | lr 0.00000 | loss 2.50765
Epoch 97 | lr 0.00000 | loss 2.39896
Epoch 97 | lr 0.00000 | loss 2.46505
Epoch 97 | lr 0.00000 | loss 2.52749
Epoch 97 | lr 0.00000 | loss 2.40895
Validation loss: 2.95400
Test loss: 2.96519
Epoch 98 | lr 0.00000 | loss 2.43740
Epoch 98 | lr 0.00000 | loss 2.42547
Epoch 98 | lr 0.00000 | loss 2.65314
Epoch 98 | lr 0.00000 | loss 2.36240
Epoch 98 | lr 0.00000 | loss 2.21236
Epoch 98 | lr 0.00000 | loss 2.42001
Validation loss: 2.95400
Test loss: 2.96519
Epoch 99 | lr 0.00000 | loss 2.44869
Epoch 99 | lr 0.00000 | loss 2.41306
Epoch 99 | lr 0.00000 | loss 2.46927
Epoch 99 | lr 0.00000 | loss 2.29154
Epoch 99 | lr 0.00000 | loss 2.40120
Epoch 99 | lr 0.00000 | loss 2.36292
Validation loss: 2.95400
Test loss: 2.96519
Epoch 100 | lr 0.00000 | loss 2.51047
Epoch 100 | lr 0.00000 | loss 2.29219
Epoch 100 | lr 0.00000 | loss 2.29253
Epoch 100 | lr 0.00000 | loss 2.42894
Epoch 100 | lr 0.00000 | loss 2.38489
Epoch 100 | lr 0.00000 | loss 2.40344
Validation loss: 2.95400
Test loss: 2.96519
-----------------------------------------------------------------------------------------
Eval loss: 2.96509

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