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概述
此笔记本将演示如何使用权重归一化层以及如何提升收敛。
WeightNormalization
用于加速深度神经网络训练的一个简单的重新参数化:
Tim Salimans、Diederik P. Kingma (2016)
通过以这种方式重新参数化权重,我们改善了优化问题的条件,并加快了随机梯度下降的收敛速度。我们的重新参数化受到批次归一化的启发,但没有在 minibatch 中的样本之间引入任何依赖关系。这意味着我们的方法也可以成功应用于循环模型(例如 LSTM)和对噪声敏感的应用(例如深度强化学习或生成模型),而批次归一化则不太适合这类模型和应用。尽管我们的方法要简单得多,但它仍可以在很大程度上为完整批次归一化提供加速。另外,我们的方法计算开销较低,从而可以在相同的时间内执行更多优化步骤。

设置
pip install -q -U tensorflow-addonsimport tensorflow as tf
import tensorflow_addons as tfa
import numpy as np
from matplotlib import pyplot as plt
# Hyper Parameters
batch_size = 32
epochs = 10
num_classes=10
构建模型
# Standard ConvNet
reg_model = tf.keras.Sequential([
tf.keras.layers.Conv2D(6, 5, activation='relu'),
tf.keras.layers.MaxPooling2D(2, 2),
tf.keras.layers.Conv2D(16, 5, activation='relu'),
tf.keras.layers.MaxPooling2D(2, 2),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(120, activation='relu'),
tf.keras.layers.Dense(84, activation='relu'),
tf.keras.layers.Dense(num_classes, activation='softmax'),
])
# WeightNorm ConvNet
wn_model = tf.keras.Sequential([
tfa.layers.WeightNormalization(tf.keras.layers.Conv2D(6, 5, activation='relu')),
tf.keras.layers.MaxPooling2D(2, 2),
tfa.layers.WeightNormalization(tf.keras.layers.Conv2D(16, 5, activation='relu')),
tf.keras.layers.MaxPooling2D(2, 2),
tf.keras.layers.Flatten(),
tfa.layers.WeightNormalization(tf.keras.layers.Dense(120, activation='relu')),
tfa.layers.WeightNormalization(tf.keras.layers.Dense(84, activation='relu')),
tfa.layers.WeightNormalization(tf.keras.layers.Dense(num_classes, activation='softmax')),
])
加载数据
(x_train, y_train), (x_test, y_test) = tf.keras.datasets.cifar10.load_data()
# Convert class vectors to binary class matrices.
y_train = tf.keras.utils.to_categorical(y_train, num_classes)
y_test = tf.keras.utils.to_categorical(y_test, num_classes)
x_train = x_train.astype('float32')
x_test = x_test.astype('float32')
x_train /= 255
x_test /= 255
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训练模型
reg_model.compile(optimizer='adam',
loss='categorical_crossentropy',
metrics=['accuracy'])
reg_history = reg_model.fit(x_train, y_train,
batch_size=batch_size,
epochs=epochs,
validation_data=(x_test, y_test),
shuffle=True)
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ETA: 0s - loss: 1.1467 - accuracy: 0.5948 1377/1563 [=========================>....] - ETA: 0s - loss: 1.1465 - accuracy: 0.5948 1400/1563 [=========================>....] - ETA: 0s - loss: 1.1461 - accuracy: 0.5945 1422/1563 [==========================>...] - ETA: 0s - loss: 1.1475 - accuracy: 0.5940 1444/1563 [==========================>...] - ETA: 0s - loss: 1.1467 - accuracy: 0.5938 1466/1563 [===========================>..] - ETA: 0s - loss: 1.1476 - accuracy: 0.5935 1488/1563 [===========================>..] - ETA: 0s - loss: 1.1465 - accuracy: 0.5938 1510/1563 [===========================>..] - ETA: 0s - loss: 1.1462 - accuracy: 0.5940 1531/1563 [============================>.] - ETA: 0s - loss: 1.1464 - accuracy: 0.5939 1553/1563 [============================>.] - ETA: 0s - loss: 1.1464 - accuracy: 0.5937 1563/1563 [==============================] - 4s 3ms/step - loss: 1.1465 - accuracy: 0.5939 - val_loss: 1.2135 - val_accuracy: 0.5650 Epoch 5/10 1/1563 [..............................] - 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ETA: 0s - loss: 1.0891 - accuracy: 0.6155 1563/1563 [==============================] - 4s 3ms/step - loss: 1.0887 - accuracy: 0.6156 - val_loss: 1.1859 - val_accuracy: 0.5871 Epoch 6/10 1/1563 [..............................] - ETA: 0s - loss: 1.2335 - accuracy: 0.5312 23/1563 [..............................] - ETA: 3s - loss: 1.1123 - accuracy: 0.5842 45/1563 [..............................] - ETA: 3s - loss: 1.0308 - accuracy: 0.6187 66/1563 [>.............................] - ETA: 3s - loss: 1.0055 - accuracy: 0.6345 87/1563 [>.............................] - ETA: 3s - loss: 1.0041 - accuracy: 0.6394 109/1563 [=>............................] - ETA: 3s - loss: 1.0050 - accuracy: 0.6408 131/1563 [=>............................] - ETA: 3s - loss: 1.0148 - accuracy: 0.6415 153/1563 [=>............................] - ETA: 3s - loss: 1.0108 - accuracy: 0.6434 175/1563 [==>...........................] - ETA: 3s - loss: 1.0191 - accuracy: 0.6391 197/1563 [==>...........................] - ETA: 3s - 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ETA: 0s - loss: 1.0322 - accuracy: 0.6339 1526/1563 [============================>.] - ETA: 0s - loss: 1.0325 - accuracy: 0.6336 1548/1563 [============================>.] - ETA: 0s - loss: 1.0321 - accuracy: 0.6338 1563/1563 [==============================] - 4s 3ms/step - loss: 1.0320 - accuracy: 0.6338 - val_loss: 1.1298 - val_accuracy: 0.6070 Epoch 7/10 1/1563 [..............................] - ETA: 0s - loss: 1.0098 - accuracy: 0.6250 22/1563 [..............................] - ETA: 3s - loss: 0.9874 - accuracy: 0.6491 44/1563 [..............................] - ETA: 3s - loss: 0.9846 - accuracy: 0.6562 65/1563 [>.............................] - ETA: 3s - loss: 0.9783 - accuracy: 0.6572 87/1563 [>.............................] - ETA: 3s - loss: 0.9731 - accuracy: 0.6552 109/1563 [=>............................] - ETA: 3s - loss: 0.9707 - accuracy: 0.6557 131/1563 [=>............................] - ETA: 3s - loss: 0.9732 - accuracy: 0.6546 152/1563 [=>............................] - 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ETA: 1s - loss: 0.8974 - accuracy: 0.6813 1118/1563 [====================>.........] - ETA: 1s - loss: 0.8998 - accuracy: 0.6806 1140/1563 [====================>.........] - ETA: 0s - loss: 0.9000 - accuracy: 0.6804 1162/1563 [=====================>........] - ETA: 0s - loss: 0.9010 - accuracy: 0.6798 1184/1563 [=====================>........] - ETA: 0s - loss: 0.9012 - accuracy: 0.6802 1206/1563 [======================>.......] - ETA: 0s - loss: 0.9019 - accuracy: 0.6799 1228/1563 [======================>.......] - ETA: 0s - loss: 0.9026 - accuracy: 0.6799 1249/1563 [======================>.......] - ETA: 0s - loss: 0.9028 - accuracy: 0.6795 1271/1563 [=======================>......] - ETA: 0s - loss: 0.9032 - accuracy: 0.6794 1294/1563 [=======================>......] - ETA: 0s - loss: 0.9061 - accuracy: 0.6785 1317/1563 [========================>.....] - ETA: 0s - loss: 0.9068 - accuracy: 0.6784 1339/1563 [========================>.....] - ETA: 0s - loss: 0.9082 - accuracy: 0.6781 1361/1563 [=========================>....] - ETA: 0s - loss: 0.9075 - accuracy: 0.6782 1383/1563 [=========================>....] - ETA: 0s - loss: 0.9068 - accuracy: 0.6785 1405/1563 [=========================>....] - ETA: 0s - loss: 0.9071 - accuracy: 0.6783 1427/1563 [==========================>...] - ETA: 0s - loss: 0.9065 - accuracy: 0.6787 1449/1563 [==========================>...] - ETA: 0s - loss: 0.9068 - accuracy: 0.6787 1471/1563 [===========================>..] - ETA: 0s - loss: 0.9067 - accuracy: 0.6785 1493/1563 [===========================>..] - ETA: 0s - loss: 0.9064 - accuracy: 0.6785 1516/1563 [============================>.] - ETA: 0s - loss: 0.9056 - accuracy: 0.6789 1538/1563 [============================>.] - ETA: 0s - loss: 0.9060 - accuracy: 0.6787 1560/1563 [============================>.] - ETA: 0s - loss: 0.9066 - accuracy: 0.6785 1563/1563 [==============================] - 4s 3ms/step - loss: 0.9070 - accuracy: 0.6784 - val_loss: 1.1235 - val_accuracy: 0.6168 Epoch 10/10 1/1563 [..............................] - ETA: 0s - loss: 0.7256 - accuracy: 0.6875 23/1563 [..............................] - ETA: 3s - loss: 0.8594 - accuracy: 0.7024 45/1563 [..............................] - ETA: 3s - loss: 0.8833 - accuracy: 0.6986 68/1563 [>.............................] - ETA: 3s - loss: 0.8942 - accuracy: 0.6898 90/1563 [>.............................] - ETA: 3s - loss: 0.8828 - accuracy: 0.6941 112/1563 [=>............................] - ETA: 3s - loss: 0.8777 - accuracy: 0.6961 134/1563 [=>............................] - ETA: 3s - loss: 0.8771 - accuracy: 0.6950 156/1563 [=>............................] - ETA: 3s - loss: 0.8709 - accuracy: 0.6957 177/1563 [==>...........................] - ETA: 3s - loss: 0.8714 - accuracy: 0.6962 199/1563 [==>...........................] - ETA: 3s - loss: 0.8704 - accuracy: 0.6960 221/1563 [===>..........................] - ETA: 3s - loss: 0.8661 - accuracy: 0.6977 243/1563 [===>..........................] - ETA: 3s - loss: 0.8647 - accuracy: 0.6986 265/1563 [====>.........................] - 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ETA: 0s - loss: 0.8811 - accuracy: 0.6884 1336/1563 [========================>.....] - ETA: 0s - loss: 0.8816 - accuracy: 0.6885 1358/1563 [=========================>....] - ETA: 0s - loss: 0.8817 - accuracy: 0.6885 1380/1563 [=========================>....] - ETA: 0s - loss: 0.8819 - accuracy: 0.6881 1402/1563 [=========================>....] - ETA: 0s - loss: 0.8818 - accuracy: 0.6882 1424/1563 [==========================>...] - ETA: 0s - loss: 0.8815 - accuracy: 0.6885 1445/1563 [==========================>...] - ETA: 0s - loss: 0.8819 - accuracy: 0.6884 1467/1563 [===========================>..] - ETA: 0s - loss: 0.8814 - accuracy: 0.6885 1489/1563 [===========================>..] - ETA: 0s - loss: 0.8814 - accuracy: 0.6886 1511/1563 [============================>.] - ETA: 0s - loss: 0.8805 - accuracy: 0.6889 1533/1563 [============================>.] - ETA: 0s - loss: 0.8800 - accuracy: 0.6891 1555/1563 [============================>.] - ETA: 0s - loss: 0.8798 - accuracy: 0.6890 1563/1563 [==============================] - 4s 3ms/step - loss: 0.8794 - accuracy: 0.6892 - val_loss: 1.1383 - val_accuracy: 0.6184
wn_model.compile(optimizer='adam',
loss='categorical_crossentropy',
metrics=['accuracy'])
wn_history = wn_model.fit(x_train, y_train,
batch_size=batch_size,
epochs=epochs,
validation_data=(x_test, y_test),
shuffle=True)
Epoch 1/10 1/1563 [..............................] - ETA: 0s - loss: 2.7437 - accuracy: 0.0625 14/1563 [..............................] - ETA: 5s - loss: 2.3881 - accuracy: 0.1786 28/1563 [..............................] - ETA: 5s - loss: 2.2533 - accuracy: 0.1864 41/1563 [..............................] - ETA: 5s - loss: 2.1833 - accuracy: 0.2012 54/1563 [>.............................] - ETA: 5s - loss: 2.1291 - accuracy: 0.2245 68/1563 [>.............................] - ETA: 5s - loss: 2.1058 - accuracy: 0.2298 82/1563 [>.............................] - ETA: 5s - loss: 2.0898 - accuracy: 0.2359 96/1563 [>.............................] - ETA: 5s - loss: 2.0675 - accuracy: 0.2461 110/1563 [=>............................] - ETA: 5s - loss: 2.0420 - accuracy: 0.2580 123/1563 [=>............................] - ETA: 5s - loss: 2.0199 - accuracy: 0.2655 137/1563 [=>............................] - ETA: 5s - loss: 2.0024 - accuracy: 0.2701 151/1563 [=>............................] - ETA: 5s - 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ETA: 2s - loss: 1.6971 - accuracy: 0.3790 828/1563 [==============>...............] - ETA: 2s - loss: 1.6943 - accuracy: 0.3798 841/1563 [===============>..............] - ETA: 2s - loss: 1.6933 - accuracy: 0.3806 855/1563 [===============>..............] - ETA: 2s - loss: 1.6900 - accuracy: 0.3819 869/1563 [===============>..............] - ETA: 2s - loss: 1.6869 - accuracy: 0.3828 883/1563 [===============>..............] - ETA: 2s - loss: 1.6838 - accuracy: 0.3840 896/1563 [================>.............] - ETA: 2s - loss: 1.6808 - accuracy: 0.3853 909/1563 [================>.............] - ETA: 2s - loss: 1.6800 - accuracy: 0.3858 921/1563 [================>.............] - ETA: 2s - loss: 1.6777 - accuracy: 0.3868 933/1563 [================>.............] - ETA: 2s - loss: 1.6752 - accuracy: 0.3882 944/1563 [=================>............] - ETA: 2s - loss: 1.6727 - accuracy: 0.3892 956/1563 [=================>............] - ETA: 2s - loss: 1.6709 - accuracy: 0.3896 968/1563 [=================>............] - 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ETA: 0s - loss: 1.6082 - accuracy: 0.4128 1411/1563 [==========================>...] - ETA: 0s - loss: 1.6063 - accuracy: 0.4135 1423/1563 [==========================>...] - ETA: 0s - loss: 1.6044 - accuracy: 0.4142 1435/1563 [==========================>...] - ETA: 0s - loss: 1.6032 - accuracy: 0.4149 1447/1563 [==========================>...] - ETA: 0s - loss: 1.6021 - accuracy: 0.4152 1459/1563 [===========================>..] - ETA: 0s - loss: 1.6006 - accuracy: 0.4160 1471/1563 [===========================>..] - ETA: 0s - loss: 1.5996 - accuracy: 0.4164 1483/1563 [===========================>..] - ETA: 0s - loss: 1.5991 - accuracy: 0.4167 1495/1563 [===========================>..] - ETA: 0s - loss: 1.5978 - accuracy: 0.4172 1507/1563 [===========================>..] - ETA: 0s - loss: 1.5970 - accuracy: 0.4177 1519/1563 [============================>.] - ETA: 0s - loss: 1.5954 - accuracy: 0.4182 1531/1563 [============================>.] - ETA: 0s - loss: 1.5941 - accuracy: 0.4187 1543/1563 [============================>.] - ETA: 0s - loss: 1.5925 - accuracy: 0.4193 1555/1563 [============================>.] - ETA: 0s - loss: 1.5914 - accuracy: 0.4196 1563/1563 [==============================] - 8s 5ms/step - loss: 1.5910 - accuracy: 0.4199 - val_loss: 1.3740 - val_accuracy: 0.5097 Epoch 2/10 1/1563 [..............................] - ETA: 0s - loss: 1.3884 - accuracy: 0.5312 13/1563 [..............................] - ETA: 6s - loss: 1.3575 - accuracy: 0.5144 25/1563 [..............................] - ETA: 6s - loss: 1.3434 - accuracy: 0.5138 37/1563 [..............................] - ETA: 6s - loss: 1.3262 - accuracy: 0.5253 49/1563 [..............................] - ETA: 6s - loss: 1.3050 - accuracy: 0.5223 61/1563 [>.............................] - ETA: 6s - loss: 1.3106 - accuracy: 0.5154 73/1563 [>.............................] - ETA: 6s - loss: 1.3223 - accuracy: 0.5086 85/1563 [>.............................] - ETA: 6s - loss: 1.3349 - accuracy: 0.5040 97/1563 [>.............................] - ETA: 6s - 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7s 5ms/step - loss: 1.3134 - accuracy: 0.5292 - val_loss: 1.2580 - val_accuracy: 0.5454 Epoch 3/10 1/1563 [..............................] - ETA: 0s - loss: 0.9207 - accuracy: 0.6875 15/1563 [..............................] - ETA: 5s - loss: 1.2248 - accuracy: 0.5708 29/1563 [..............................] - ETA: 5s - loss: 1.2324 - accuracy: 0.5560 43/1563 [..............................] - ETA: 5s - loss: 1.2100 - accuracy: 0.5690 57/1563 [>.............................] - ETA: 5s - loss: 1.2137 - accuracy: 0.5652 70/1563 [>.............................] - ETA: 5s - loss: 1.2053 - accuracy: 0.5652 84/1563 [>.............................] - ETA: 5s - loss: 1.2240 - accuracy: 0.5603 98/1563 [>.............................] - ETA: 5s - loss: 1.2151 - accuracy: 0.5638 112/1563 [=>............................] - ETA: 5s - loss: 1.2212 - accuracy: 0.5625 126/1563 [=>............................] - ETA: 5s - loss: 1.2259 - accuracy: 0.5608 140/1563 [=>............................] - ETA: 5s - 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ETA: 1s - loss: 1.2009 - accuracy: 0.5712 1309/1563 [========================>.....] - ETA: 0s - loss: 1.1993 - accuracy: 0.5719 1322/1563 [========================>.....] - ETA: 0s - loss: 1.1987 - accuracy: 0.5720 1336/1563 [========================>.....] - ETA: 0s - loss: 1.1988 - accuracy: 0.5720 1350/1563 [========================>.....] - ETA: 0s - loss: 1.1989 - accuracy: 0.5717 1364/1563 [=========================>....] - ETA: 0s - loss: 1.1987 - accuracy: 0.5716 1377/1563 [=========================>....] - ETA: 0s - loss: 1.1986 - accuracy: 0.5718 1391/1563 [=========================>....] - ETA: 0s - loss: 1.1982 - accuracy: 0.5719 1404/1563 [=========================>....] - ETA: 0s - loss: 1.1980 - accuracy: 0.5719 1418/1563 [==========================>...] - ETA: 0s - loss: 1.1977 - accuracy: 0.5721 1431/1563 [==========================>...] - ETA: 0s - loss: 1.1971 - accuracy: 0.5724 1444/1563 [==========================>...] - ETA: 0s - loss: 1.1968 - accuracy: 0.5726 1457/1563 [==========================>...] - 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ETA: 0s - loss: 1.1128 - accuracy: 0.6042 1501/1563 [===========================>..] - ETA: 0s - loss: 1.1116 - accuracy: 0.6046 1515/1563 [============================>.] - ETA: 0s - loss: 1.1126 - accuracy: 0.6041 1528/1563 [============================>.] - ETA: 0s - loss: 1.1129 - accuracy: 0.6041 1542/1563 [============================>.] - ETA: 0s - loss: 1.1119 - accuracy: 0.6045 1556/1563 [============================>.] - ETA: 0s - loss: 1.1124 - accuracy: 0.6043 1563/1563 [==============================] - 7s 4ms/step - loss: 1.1125 - accuracy: 0.6043 - val_loss: 1.1817 - val_accuracy: 0.5820 Epoch 5/10 1/1563 [..............................] - ETA: 0s - loss: 1.0670 - accuracy: 0.6250 15/1563 [..............................] - ETA: 5s - loss: 1.0495 - accuracy: 0.6396 29/1563 [..............................] - ETA: 5s - loss: 1.0295 - accuracy: 0.6466 43/1563 [..............................] - ETA: 5s - loss: 1.0389 - accuracy: 0.6344 56/1563 [>.............................] - 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ETA: 0s - loss: 0.9050 - accuracy: 0.6808 1555/1563 [============================>.] - ETA: 0s - loss: 0.9042 - accuracy: 0.6809 1563/1563 [==============================] - 7s 4ms/step - loss: 0.9040 - accuracy: 0.6810 - val_loss: 1.1338 - val_accuracy: 0.6137 Epoch 9/10 1/1563 [..............................] - ETA: 0s - loss: 0.8992 - accuracy: 0.6562 15/1563 [..............................] - ETA: 5s - loss: 0.8471 - accuracy: 0.6979 29/1563 [..............................] - ETA: 5s - loss: 0.7931 - accuracy: 0.7166 43/1563 [..............................] - ETA: 5s - loss: 0.8113 - accuracy: 0.7144 57/1563 [>.............................] - ETA: 5s - loss: 0.8083 - accuracy: 0.7155 70/1563 [>.............................] - ETA: 5s - loss: 0.7957 - accuracy: 0.7205 83/1563 [>.............................] - ETA: 5s - loss: 0.8101 - accuracy: 0.7097 97/1563 [>.............................] - ETA: 5s - loss: 0.8047 - accuracy: 0.7152 111/1563 [=>............................] - ETA: 5s - 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7s 4ms/step - loss: 0.8686 - accuracy: 0.6927 - val_loss: 1.1266 - val_accuracy: 0.6156 Epoch 10/10 1/1563 [..............................] - ETA: 0s - loss: 0.9575 - accuracy: 0.7188 14/1563 [..............................] - ETA: 5s - loss: 0.7337 - accuracy: 0.7478 27/1563 [..............................] - ETA: 5s - loss: 0.7710 - accuracy: 0.7396 40/1563 [..............................] - ETA: 5s - loss: 0.8051 - accuracy: 0.7227 53/1563 [>.............................] - ETA: 5s - loss: 0.8066 - accuracy: 0.7229 66/1563 [>.............................] - ETA: 5s - loss: 0.7986 - accuracy: 0.7249 79/1563 [>.............................] - ETA: 5s - loss: 0.7921 - accuracy: 0.7271 92/1563 [>.............................] - ETA: 5s - loss: 0.8068 - accuracy: 0.7228 105/1563 [=>............................] - ETA: 5s - loss: 0.7981 - accuracy: 0.7241 118/1563 [=>............................] - ETA: 5s - loss: 0.8037 - accuracy: 0.7195 131/1563 [=>............................] - ETA: 5s - 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reg_accuracy = reg_history.history['accuracy']
wn_accuracy = wn_history.history['accuracy']
plt.plot(np.linspace(0, epochs, epochs), reg_accuracy,
color='red', label='Regular ConvNet')
plt.plot(np.linspace(0, epochs, epochs), wn_accuracy,
color='blue', label='WeightNorm ConvNet')
plt.title('WeightNorm Accuracy Comparison')
plt.legend()
plt.grid(True)
plt.show()

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在 Google Colab 中运行
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