深度解析Droupout与Batch Normalization
Droupout与Batch Normalization都是深度学习常用且基础的训练技巧了。本文将从理论和实践两个角度分布其特点和细节。
Droupout
2012年,Hinton在其论文中提出Dropout。当一个复杂的前馈神经网络被训练在小的数据集时,容易造成过拟合。为了防止过拟合,可以通过阻止特征检测器的共同作用来提高神经网络的性能。
Droupout是一种针对深度学习广泛应用的正则化技术。在每次迭代时随机关闭一些神经单元,随着迭代的进行,由于其他神经元可能在任何时候都被关闭,因此神经元对其他特定神经元的激活变得不那么敏感。
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" alt="Droupout">
从数学上来说,神经网络层训练过程中使用的标准 Dropout 的行为可以被写作:
\]
其中 \(f(·)\)为激活函数,\(x\) 是该层的输入,\(W\) 是该层的权值矩阵,\(y\)为该层的输出,而 \(m\) 则为该层的 Dropout 掩膜(mask),mask 中每个元素为 1 的概率为 \(p\)。在测试阶段,该层的输出可以被写作:
\]
Q&A
为什么说Dropout可以解决过拟合?
(1)取平均的作用。dropout掉不同的隐藏神经元就类似在训练不同的网络,随机删掉一半隐藏神经元导致网络结构已经不同,整个dropout过程就相当于对很多个不同的神经网络取平均。而不同的网络产生不同的过拟合,一些互为“反向”的拟合相互抵消就可以达到整体上减少过拟合。
(2)减少神经元之间复杂的共适应关系: 因为dropout程序导致两个神经元不一定每次都在一个dropout网络中出现。这样权值的更新不再依赖于有固定关系的隐含节点的共同作用,阻止了某些特征仅仅在其它特定特征下才有效果的情况 。迫使网络去学习更加鲁棒的特征 ,这些特征在其它的神经元的随机子集中也存在。换句话说假如我们的神经网络是在做出某种预测,它不应该对一些特定的线索片段太过敏感,即使丢失特定的线索,它也应该可以从众多其它线索中学习一些共同的特征。从这个角度看dropout就有点像L1,L2正则,减少权重使得网络对丢失特定神经元连接的鲁棒性提高。
(3)Dropout类似于性别在生物进化中的角色:物种为了生存往往会倾向于适应这种环境,环境突变则会导致物种难以做出及时反应,性别的出现可以繁衍出适应新环境的变种,有效的阻止过拟合,即避免环境改变时物种可能面临的灭绝。
类比于Bagging方法,Dropout可被认为是一种实用的大规模深度神经网络的模型集成算法。这是由于传统意义上的Bagging涉及多个模型的同时训练与测试评估,当网络与参数规模庞大时,这种集成方式需要消耗大量的运算时间与空间。Dropout在小批量级别上的操作,提供了一种轻量级的Bagging集成近似,能够实现指数级数量神经网络的训练与评测。
Dropout缺点
明确定义的损失函数每一次迭代都会下降,而dropout每一次都会随机删除节点,也就是说每一次训练的网络都是不同的,损失函数不再被明确地定义,在某种程度上很难计算,我们失去了调试工具。
如何使用 Dropout
Dropout存在两个版本:Vanilla Dropout 和 Inverted Dropout。(这里只对Inverted Dropout进行说明)
对于inverted dropout,在训练阶段期间对激活值进行缩放,而测试阶段保持不变。这是因为当模型使用了dropout layer,训练的时候只有占比为\(p\)的隐藏层单元参与训练,那么在预测的时候,如果所有的隐藏层单元都需要参与进来,则得到的结果是训练时的\(\frac{1}{p}\)倍 ,为了避免这种情况,就需要测试的时候将输出结果乘以\(p\) 使下一层的输入规模保持不变。而利用inverted dropout,我们可以在训练的时候直接将dropout后留下的权重扩大\(\frac{1}{p}\)倍,这样就可以使结果的scale保持不变,而在预测的时候也不用做额外的操作了。
ResNet为什么不用Dropout?
Dropout与BN不兼容;同时,BN在训练过程对每个单个样本的forward均引入多个样本(Batch个)的统计信息,相当于自带一定噪音,起到正则效果,所以也就基本消除了Dropout的必要。
Dropout实现
这里使用numpy实现了一个普通的神经网络如何在训练中,利用Dropout的keep_out进行前向和反向传播。
import numpy as np
def forward_propagation_with_dropout(X, parameters, keep_prob=0.5):
"""
Implements the forward propagation: LINEAR -> RELU + DROPOUT -> LINEAR -> RELU + DROPOUT -> LINEAR -> SIGMOID.
"""
np.random.seed(1)
# retrieve parameters
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
W3 = parameters["W3"]
b3 = parameters["b3"]
Z1 = np.dot(W1, X) + b1
A1 = relu(Z1)
D1 = np.random.rand(A1.shape[0], A1.shape[1])
D1 = (D1 < keep_prob)
A1 = A1 * D1
A1 = A1 / keep_prob
Z2 = np.dot(W2, A1) + b2
A2 = relu(Z2)
D2 = np.random.rand(A2.shape[0], A1.shape[1])
D2 = (D2 < keep_prob)
A2 = A2 * D2
A2 = A2 / keep_prob
Z3 = np.dot(W3, A2) + b3
A3 = sigmoid(Z3)
cache = (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3)
return A3, cache
# GRADED FUNCTION: backward_propagation_with_dropout
def backward_propagation_with_dropout(X, Y, cache, keep_prob):
"""
Implements the backward propagation of our baseline model to which we added dropout.
"""
m = X.shape[1]
(Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3) = cache
dZ3 = A3 - Y
dW3 = 1. / m * np.dot(dZ3, A2.T)
db3 = 1. / m * np.sum(dZ3, axis=1, keepdims=True)
dA2 = np.dot(W3.T, dZ3)
dA2 *= D2
dA2 = dA2 / keep_prob
dZ2 = np.multiply(dA2, np.int64(A2 > 0))
dW2 = 1. / m * np.dot(dZ2, A1.T)
db2 = 1. / m * np.sum(dZ2, axis=1, keepdims=True)
dA1 = np.dot(W2.T, dZ2)
dA1 *= D1
dA1 /= keep_prob
dZ1 = np.multiply(dA1, np.int64(A1 > 0))
dW1 = 1. / m * np.dot(dZ1, X.T)
db1 = 1. / m * np.sum(dZ1, axis=1, keepdims=True)
gradients = {"dZ3": dZ3, "dW3": dW3, "db3": db3, "dA2": dA2,
"dZ2": dZ2, "dW2": dW2, "db2": db2, "dA1": dA1,
"dZ1": dZ1, "dW1": dW1, "db1": db1}
return gradients
Batch Normalization
Batch Normalization, 批标准化, 和普通的数据标准化类似, 是将分散的数据统一的一种做法, 也是优化神经网络的一种方法.
在深度学习中,由于问题的复杂性,尤其是对深层神经网络的训练调参是困难且复杂的。在这个过程中,我们需要去尝试不同的学习率、初始化参数方法(例如Xavier初始化)等方式来帮助我们的模型加速收敛。深度神经网络之所以如此难训练,其中一个重要原因就是网络中层与层之间存在高度的关联性与耦合性。在训练中,网络中层与层之间的关联性会导致如下的状况:随着训练的进行,网络中的参数也随着梯度下降在不停更新。一方面,当底层网络中参数发生微弱变化时,由于每一层中的线性变换与非线性激活映射,这些微弱变化随着网络层数的加深而被放大(类似蝴蝶效应);另一方面,参数的变化导致每一层的输入分布会发生改变,进而上层的网络需要不停地去适应这些分布变化,使得我们的模型训练变得困难。上述这一现象叫做Internal Covariate Shift。
Batch Normalization的原论文作者给了Internal Covariate Shift一个较规范的定义:在深层网络训练的过程中,由于网络中参数变化而引起内部结点数据分布发生变化的这一过程被称作Internal Covariate Shift。
Internal Covariate Shift会带来什么问题?
(1)上层网络需要不停调整来适应输入数据分布的变化,导致网络学习速度的降低
(2)网络的训练过程容易陷入梯度饱和区,减缓网络收敛速度
当我们在神经网络中采用饱和激活函数(saturated activation function)时,例如sigmoid,tanh激活函数,很容易使得模型训练陷入梯度饱和区(saturated regime)。对于激活函数梯度饱和问题,有两种解决思路。第一种就是更为非饱和性激活函数,例如线性整流函数ReLU可以在一定程度上解决训练进入梯度饱和区的问题。另一种思路是,我们可以让激活函数的输入分布保持在一个稳定状态来尽可能避免它们陷入梯度饱和区,这也就是Normalization的思路。
那我们如何减缓Internal Covariate Shift?ICS产生的原因是由于参数更新带来的网络中每一层输入值分布的改变,并且随着网络层数的加深而变得更加严重,因此我们可以通过固定每一层网络输入值的分布来对减缓ICS问题。
(1)白化(Whitening)。白化是对输入数据分布进行变换,进而达到以下两个目的:
第一,使得输入特征分布具有相同的均值与方差。其中PCA白化保证了所有特征分布均值为0,方差为1;而ZCA白化则保证了所有特征分布均值为0,方差相同;
第二,去除特征之间的相关性。通过白化操作,我们可以减缓ICS的问题,进而固定了每一层网络输入分布,加速网络训练过程的收敛。
(2)Batch Normalization。白化过程计算成本太高,并且由于改变了网络每一层的分布,因而改变了网络层中本身数据的表达能力。底层网络学习到的参数信息会被白化操作丢失掉。
在深度学习中,由于采用full batch的训练方式对内存要求较大,且每一轮训练时间过长;我们一般都会采用对数据做划分,用mini-batch对网络进行训练。因此,Batch Normalization也就在mini-batch的基础上进行计算。
通过对每一个神经元输出值减去一个batch的均值,除以方差,我们可以用更加简化的方式来对数据进行规范化,即:
\sigma_j^2 = \frac{1}{m} \sum_{i=1}^m (Z_j^{(i)}-\mu_j)^2 \\
\hat{Z_j}=\frac{Z_j - \mu_j}{ \sqrt{\sigma_j^2 + \epsilon}}
\]
其中\(\epsilon\)是为了防止方差为0产生无效计算。
使得每一层的输入每个特征的分布均值为0,方差为1。但这样但却导致了数据表达能力的缺失。也就是我们通过变换操作改变了原有数据的信息表达(representation ability of the network),使得底层网络学习到的参数信息丢失。另一方面,通过让每一层的输入分布均值为0,方差为1,会使得输入在经过sigmoid或tanh激活函数时,容易陷入非线性激活函数的线性区域。
因此,BN又引入了两个可学习(learnable)的参数\(\gamma\)与\(\beta\) 。这两个参数的引入是为了恢复数据本身的表达能力,对规范化后的数据进行线性变换,即:
\]
特别地,当\(\gamma^2=\sigma^2,\beta=\mu\)时,可以实现等价变换(identity transform)并且保留了原始输入特征的分布信息。
通过上面的步骤,我们就在一定程度上保证了输入数据的表达能力。
以上就是整个Batch Normalization在模型训练中的算法和思路。
补充: 在进行normalization的过程中,由于我们的规范化操作会对减去均值,因此,偏置项 \(b\) 可以被忽略掉或可以被置为0
总结一下,BN的作用与问题:
BN的作用:
(1)允许较大的学习率;
(2)减弱对初始化的强依赖性
(3)保持隐藏层中数值的均值、方差不变,让数值更稳定,为后面网络提供坚实的基础;
(4)有轻微的正则化作用(相当于给隐藏层加入噪声,类似Dropout)
BN存在的问题:
(1)每次是在一个batch上计算均值、方差,如果batch size太小,则计算的均值、方差不足以代表整个数据分布。
(2)batch size太大:会超过内存容量;需要跑更多的epoch,导致总训练时间变长;会直接固定梯度下降的方向,导致很难更新。
Q&A
测试阶段如何使用Batch Normalization?
利用BN训练好模型后,我们保留了每组mini-batch训练数据在网络中每一层的 \(\mu_{batch}\) 与 \(\sigma_{batch}^2\)。
此时我们使用整个样本的统计量来对Test数据进行归一化,具体来说使用均值与方差的无偏估计:
\sigma_{test}^2 = \frac{m}{m-1}E(\sigma_{btach}^2) \\
\]
得到每个特征的均值与方差的无偏估计后,我们对test数据采用同样的normalization方法:
\]
另外,除了采用整体样本的无偏估计外。吴恩达在Coursera上的Deep Learning课程指出可以对train阶段每个batch计算的mean/variance采用指数加权平均来得到test阶段mean/variance的估计。
BN训练时为什么不用全量训练集的均值和方差呢?
因为用全量训练集的均值和方差容易过拟合,对于BN,其实就是对每一批数据进行归一化到一个相同的分布,而每一批数据的均值和方差会有一定的差别,而不是用固定的值,这个差别实际上能够增加模型的鲁棒性,也会在一定程度上减少过拟合。
也正是因此,BN一般要求将训练集完全打乱,并用一个较大的batch值,否则,一个batch的数据无法较好得代表训练集的分布,会影响模型训练的效果。
Batch Normalization的优势
Batch Normalization在实际工程中被证明了能够缓解神经网络难以训练的问题,BN具有的优势可以总结为以下几点:
(1)BN使得网络中每层输入数据的分布相对稳定,加速模型学习速度
BN通过规范化与线性变换使得每一层网络的输入数据的均值与方差都在一定范围内,使得后一层网络不必不断去适应底层网络中输入的变化,从而实现了网络中层与层之间的解耦,允许每一层进行独立学习,有利于提高整个神经网络的学习速度。
(2)BN使得模型对网络中的参数不那么敏感,简化调参过程,使得网络学习更加稳定
在神经网络中,我们经常会谨慎地采用一些权重初始化方法(例如Xavier)或者合适的学习率来保证网络稳定训练。
当学习率设置太高时,会使得参数更新步伐过大,容易出现震荡和不收敛。但是使用BN的网络将不会受到参数数值大小的影响。在使用Batch Normalization之后,抑制了参数微小变化随着网络层数加深被放大的问题,使得网络对参数大小的适应能力更强,此时我们可以设置较大的学习率而不用过于担心模型divergence的风险。
(3)BN允许网络使用饱和性激活函数(例如sigmoid,tanh等),缓解梯度消失问题
在不使用BN层的时候,由于网络的深度与复杂性,很容易使得底层网络变化累积到上层网络中,导致模型的训练很容易进入到激活函数的梯度饱和区;通过normalize操作可以让激活函数的输入数据落在梯度非饱和区,缓解梯度消失的问题;另外通过自适应学习\(\gamma\)与\(\beta\)又让数据保留更多的原始信息。
(4)BN具有一定的正则化效果
在Batch Normalization中,由于我们使用mini-batch的均值与方差作为对整体训练样本均值与方差的估计,尽管每一个batch中的数据都是从总体样本中抽样得到,但不同mini-batch的均值与方差会有所不同,这就为网络的学习过程中增加了随机噪音,与Dropout通过关闭神经元给网络训练带来噪音类似,在一定程度上对模型起到了正则化的效果。
Batch Normalization训练注意事项
tf.layers.batch_normalization接口中training参数非常重要。当我们训练时,要设置为True,保证在训练过程中使用的是mini-batch的统计量进行normalization;在Inference阶段,使用False,也就是使用总体样本的无偏估计。另外,当self.use_batch_norm为True时,要使用tf.control_dependencies保证模型正常训练。
Batch-normalized 应该放在非线性激活层的前面还是后面?
在BN的原始论文中,BN是放在非线性激活层前面的。但目前在实践上,倾向于把BN放在ReLU后面。 Batch-Normalization可以视作对传给隐藏层的输入的normalization。BN层的作用机制也许是通过平滑隐藏层输入的分布,帮助随机梯度下降的进行,缓解随机梯度下降权重更新对后续层的负面影响。因此,实际上,无论是放非线性激活之前,还是之后,也许都能发挥这个作用。只不过,取决于具体激活函数的不同,效果也许有一点差别(比如,对sigmoid和tanh而言,放非线性激活之前,也许顺便还能缓解sigmoid/tanh的梯度衰减问题,而对ReLU而言,这个平滑作用经ReLU“扭曲”之后也许有所衰弱)。
BN和Dropout共同使用时会出现的问题
BN和Dropout单独使用都能减少过拟合并加速训练速度,但如果一起使用的话并不会产生1+1>2的效果,相反可能会得到比单独使用更差的效果。
理解 Dropout 与 BN 之间冲突的关键是网络状态切换过程中存在神经方差的(neural variance)不一致行为。试想若有图一中的神经响应 X,当网络从训练转为测试时,Dropout 可以通过其随机失活保留率(即 p)来缩放响应,并在学习中改变神经元的方差,而 BN 仍然维持 X 的统计滑动方差。这种方差不匹配可能导致数值不稳定(见下图中的红色曲线)。而随着网络越来越深,最终预测的数值偏差可能会累计,从而降低系统的性能。简单起见,作者们将这一现象命名为「方差偏移」。事实上,如果没有 Dropout,那么实际前馈中的神经元方差将与 BN 所累计的滑动方差非常接近(见下图中的蓝色曲线),这也保证了其较高的测试准确率。
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" alt="BN和Dropout共同使用时会出现的问题">
作者采用了两种策略来探索如何打破这种局限。一个是在所有 BN 层后使用 Dropout,另一个就是修改 Dropout 的公式让它对方差并不那么敏感,就是高斯Dropout。
第一个方案比较简单,把Dropout放在所有BN层的后面就可以了,这样就不会产生方差偏移的问题,但实则有逃避问题的感觉。
第二个方案来自Dropout原文里提到的一种高斯Dropout,是对Dropout形式的一种拓展。作者进一步拓展了高斯Dropout,提出了一个均匀分布Dropout,这样做带来了一个好处就是这个形式的Dropout(又称为“Uout”)对方差的偏移的敏感度降低了,总得来说就是整体方差偏地没有那么厉害了。
论文:Improving neural networks by preventing co-adaptation of feature detectors
论文:Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
论文:Understanding the Disharmony between Dropout and Batch Normalization by Variance Shift
深度学习中Dropout原理解析
Batch Normalization原理与实战
Batch-normalized 应该放在非线性激活层的前面还是后面?
BN和Dropout在训练和测试时的差别
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