本文主要是介绍maxout简单理解，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
maxout出现在ICML2013上，作者Goodfellow将maxout和dropout结合后，号称在MNIST, CIFAR-10, CIFAR-100, SVHN这4个数据上都取得了start-of-art的识别率。
从论文中可以看出，maxout其实一种激发函数形式。通常情况下，如果激发函数采用sigmoid函数的话，在前向传播过程中，隐含层节点的输出表达式为：
其中W一般是2维的，这里表示取出的是第i列，下标i前的省略号表示对应第i列中的所有行。但如果是maxout激发函数，则其隐含层节点的输出表达式为：
这里的W是3维的，尺寸为d*m*k，其中d表示输入层节点的个数，m表示隐含层节点的个数，k表示每个隐含层节点对应了k个”隐隐含层”节点，这k个”隐隐含层”节点都是线性输出的，而maxout的每个节点就是取这k个”隐隐含层”节点输出值中最大的那个值。因为激发函数中有了max操作，所以整个maxout网络也是一种非线性的变换。因此当我们看到常规结构的神经网络时，如果它使用了maxout激发，则我们头脑中应该自动将这个”隐隐含层”节点加入。参考一个日文的maxout ppt 中的一页ppt如下：
ppt中箭头前后示意图大家应该可以明白什么是maxout激发函数了。
maxout的拟合能力是非常强的，它可以拟合任意的的凸函数。最直观的解释就是任意的凸函数都可以由分段线性函数以任意精度拟合（学过高等数学应该能明白），而maxout又是取k个隐隐含层节点的最大值，这些”隐隐含层"节点也是线性的，所以在不同的取值范围下，最大值也可以看做是分段线性的（分段的个数与k值有关）。论文中的图1如下（它表达的意思就是可以拟合任意凸函数，当然也包括了ReLU了）：
作者从数学的角度上也证明了这个结论，即只需2个maxout节点就可以拟合任意的凸函数了（相减），前提是”隐隐含层”节点的个数可以任意多，如下图所示：
下面来看下maxout源码，看其激发函数表达式是否符合我们的理解。找到库目录下的pylearn2/models/maxout.py文件，选择不带卷积的Maxout类，主要是其前向传播函数fprop():
def fprop(self, state_below): #前向传播，对linear分组进行max-pooling操作self.input_space.validate(state_below)if self.requires_reformat:if not isinstance(state_below, tuple):for sb in get_debug_values(state_below):if sb.shape[0] != self.dbm.batch_size:raise ValueError("self.dbm.batch_size is %d but got shape of %d" % (self.dbm.batch_size, sb.shape[0]))assert reduce(lambda x,y: x * y, sb.shape[1:]) == self.input_dimstate_below = self.input_space.format_as(state_below, self.desired_space) #统一好输入数据的格式z = self.transformer.lmul(state_below) + self.b # lmul()函数返回的是 return T.dot(x, self._W)if not hasattr(self, 'randomize_pools'):self.randomize_pools = Falseif not hasattr(self, 'pool_stride'):self.pool_stride = self.pool_size #默认情况下是没有重叠的poolingif self.randomize_pools:z = T.dot(z, self.permute)if not hasattr(self, 'min_zero'):self.min_zero = Falseif self.min_zero:p = T.zeros_like(z) #返回一个和z同样大小的矩阵，元素值为0,元素值类型和z的类型一样else:p = Nonelast_start = self.detector_layer_dim - self.pool_sizefor i in xrange(self.pool_size): #xrange和reange的功能类似cur = z[:,i:last_start+i+1:self.pool_stride] # L[start:end:step]是用来切片的，从[start,end)之间，每隔step取一次if p is None:p = curelse:p = T.maximum(cur, p) #将p进行迭代比较，因为每次取的是每个group里的元素，所以进行pool_size次后就可以获得每个group的最大值p.name = self.layer_name + '_p_'return p
仔细阅读上面的源码，发现和文章中描述基本是一致的，只是多了很多细节。
由于没有GPU，所以只用CPU 跑了个mnist的简单实验，参考：maxout下的readme文件。(需先下载mnist dataset到PYLEARN2_DATA_PATA目录下)。
执行../../train.py minist_pi.yaml
此时的.yaml配置文件内容如下：
!obj:pylearn2.train.Train {dataset: &train !obj:pylearn2.datasets.mnist.MNIST {which_set: 'train',one_hot: 1,start: 0,stop: 50000},model: !obj:pylearn2.models.mlp.MLP {layers: [!obj:pylearn2.models.maxout.Maxout {layer_name: 'h0',num_units: 240,num_pieces: 5,irange: .005,max_col_norm: 1.9365,},!obj:pylearn2.models.maxout.Maxout {layer_name: 'h1',num_units: 240,num_pieces: 5,irange: .005,max_col_norm: 1.9365,},!obj:pylearn2.models.mlp.Softmax {max_col_norm: 1.9365,layer_name: 'y',n_classes: 10,irange: .005}],nvis: 784,},algorithm: !obj:pylearn2.training_algorithms.sgd.SGD {batch_size: 100,learning_rate: .1,learning_rule: !obj:pylearn2.training_algorithms.learning_rule.Momentum {init_momentum: .5,},monitoring_dataset:{'train' : *train,'valid' : !obj:pylearn2.datasets.mnist.MNIST {which_set: 'train',one_hot: 1,start: 50000,stop: 60000},'test' : !obj:pylearn2.datasets.mnist.MNIST {which_set: 'test',one_hot: 1,}},cost: !obj:pylearn2.costs.mlp.dropout.Dropout {input_include_probs: { 'h0' : .8 },input_scales: { 'h0': 1. }},termination_criterion: !obj:pylearn2.termination_criteria.MonitorBased {channel_name: "valid_y_misclass",prop_decrease: 0.,N: 100},update_callbacks: !obj:pylearn2.training_algorithms.sgd.ExponentialDecay {decay_factor: 1.000004,min_lr: .000001}},extensions: [!obj:pylearn2.train_extensions.best_params.MonitorBasedSaveBest {channel_name: 'valid_y_misclass',save_path: "${PYLEARN2_TRAIN_FILE_FULL_STEM}_best.pkl"},!obj:pylearn2.training_algorithms.learning_rule.MomentumAdjustor {start: 1,saturate: 250,final_momentum: .7}],save_path: "${PYLEARN2_TRAIN_FILE_FULL_STEM}.pkl",save_freq: 1
} 跑了一个晚上才迭代了210次，被我kill掉了（笔记本还得拿到别的地方干活），这时的误差率为1.22%。估计继续跑几个小时应该会降到作者的0.94%误差率。
其monitor监控输出结果如下：
Monitoring step:Epochs seen: 210Batches seen: 105000Examples seen: 10500000learning_rate: 0.0657047371741momentum: 0.667871485944monitor_seconds_per_epoch: 121.0test_h0_col_norms_max: 1.9364999test_h0_col_norms_mean: 1.09864382902test_h0_col_norms_min: 0.0935518826938test_h0_p_max_x.max_u: 3.97355476543test_h0_p_max_x.mean_u: 2.14463905251test_h0_p_max_x.min_u: 0.961549570265test_h0_p_mean_x.max_u: 0.878285389379test_h0_p_mean_x.mean_u: 0.131020009421test_h0_p_mean_x.min_u: -0.373017504665test_h0_p_min_x.max_u: -0.202480633479test_h0_p_min_x.mean_u: -1.31821964107test_h0_p_min_x.min_u: -2.52428183099test_h0_p_range_x.max_u: 5.56309069078test_h0_p_range_x.mean_u: 3.46285869357test_h0_p_range_x.min_u: 2.01775637301test_h0_row_norms_max: 2.67556467test_h0_row_norms_mean: 1.15743973628test_h0_row_norms_min: 0.0951322935423test_h1_col_norms_max: 1.12119975186test_h1_col_norms_mean: 0.595629304226test_h1_col_norms_min: 0.183531862659test_h1_p_max_x.max_u: 6.42944749321test_h1_p_max_x.mean_u: 3.74599401756test_h1_p_max_x.min_u: 2.03028191814test_h1_p_mean_x.max_u: 1.38424650414test_h1_p_mean_x.mean_u: 0.583690886644test_h1_p_mean_x.min_u: 0.0253866100292test_h1_p_min_x.max_u: -0.830110300894test_h1_p_min_x.mean_u: -1.73539242398test_h1_p_min_x.min_u: -3.03677525979test_h1_p_range_x.max_u: 8.63650239768test_h1_p_range_x.mean_u: 5.48138644154test_h1_p_range_x.min_u: 3.36428499068test_h1_row_norms_max: 1.95904749183test_h1_row_norms_mean: 1.40561339238test_h1_row_norms_min: 1.16953677471test_objective: 0.0959691806325test_y_col_norms_max: 1.93642459019test_y_col_norms_mean: 1.90996961714test_y_col_norms_min: 1.88659811751test_y_max_max_class: 1.0test_y_mean_max_class: 0.996910632311test_y_min_max_class: 0.824416386342test_y_misclass: 0.0114test_y_nll: 0.0609837733094test_y_row_norms_max: 0.536167736581test_y_row_norms_mean: 0.386866656967test_y_row_norms_min: 0.266996530755train_h0_col_norms_max: 1.9364999train_h0_col_norms_mean: 1.09864382902train_h0_col_norms_min: 0.0935518826938train_h0_p_max_x.max_u: 3.98463017313train_h0_p_max_x.mean_u: 2.16546276053train_h0_p_max_x.min_u: 0.986865505974train_h0_p_mean_x.max_u: 0.850944629066train_h0_p_mean_x.mean_u: 0.135825383808train_h0_p_mean_x.min_u: -0.354841456train_h0_p_min_x.max_u: -0.20750516843train_h0_p_min_x.mean_u: -1.32748375925train_h0_p_min_x.min_u: -2.49716541111train_h0_p_range_x.max_u: 5.61263186775train_h0_p_range_x.mean_u: 3.49294651978train_h0_p_range_x.min_u: 2.07324073262train_h0_row_norms_max: 2.67556467train_h0_row_norms_mean: 1.15743973628train_h0_row_norms_min: 0.0951322935423train_h1_col_norms_max: 1.12119975186train_h1_col_norms_mean: 0.595629304226train_h1_col_norms_min: 0.183531862659train_h1_p_max_x.max_u: 6.49689754011train_h1_p_max_x.mean_u: 3.77637040198train_h1_p_max_x.min_u: 2.03274038543train_h1_p_mean_x.max_u: 1.34966894021train_h1_p_mean_x.mean_u: 0.57555584546train_h1_p_mean_x.min_u: 0.0176827309146train_h1_p_min_x.max_u: -0.845786992369train_h1_p_min_x.mean_u: -1.74696425227train_h1_p_min_x.min_u: -3.05703072635train_h1_p_range_x.max_u: 8.73556577905train_h1_p_range_x.mean_u: 5.52333465425train_h1_p_range_x.min_u: 3.379501944train_h1_row_norms_max: 1.95904749183train_h1_row_norms_mean: 1.40561339238train_h1_row_norms_min: 1.16953677471train_objective: 0.0119584870103train_y_col_norms_max: 1.93642459019train_y_col_norms_mean: 1.90996961714train_y_col_norms_min: 1.88659811751train_y_max_max_class: 1.0train_y_mean_max_class: 0.999958965285train_y_min_max_class: 0.996295480193train_y_misclass: 0.0train_y_nll: 4.22109408992e-05train_y_row_norms_max: 0.536167736581train_y_row_norms_mean: 0.386866656967train_y_row_norms_min: 0.266996530755valid_h0_col_norms_max: 1.9364999valid_h0_col_norms_mean: 1.09864382902valid_h0_col_norms_min: 0.0935518826938valid_h0_p_max_x.max_u: 3.970333514valid_h0_p_max_x.mean_u: 2.15548653063valid_h0_p_max_x.min_u: 0.99228626325valid_h0_p_mean_x.max_u: 0.84583547397valid_h0_p_mean_x.mean_u: 0.143554208322valid_h0_p_mean_x.min_u: -0.349097300524valid_h0_p_min_x.max_u: -0.218285757389valid_h0_p_min_x.mean_u: -1.28008164111valid_h0_p_min_x.min_u: -2.41494612443valid_h0_p_range_x.max_u: 5.54136030367valid_h0_p_range_x.mean_u: 3.43556817173valid_h0_p_range_x.min_u: 2.03580165751valid_h0_row_norms_max: 2.67556467valid_h0_row_norms_mean: 1.15743973628valid_h0_row_norms_min: 0.0951322935423valid_h1_col_norms_max: 1.12119975186valid_h1_col_norms_mean: 0.595629304226valid_h1_col_norms_min: 0.183531862659valid_h1_p_max_x.max_u: 6.4820340666valid_h1_p_max_x.mean_u: 3.75160795812valid_h1_p_max_x.min_u: 2.00587987424valid_h1_p_mean_x.max_u: 1.38777592924valid_h1_p_mean_x.mean_u: 0.578550013139valid_h1_p_mean_x.min_u: 0.0232071426066valid_h1_p_min_x.max_u: -0.84151110053valid_h1_p_min_x.mean_u: -1.73734213646valid_h1_p_min_x.min_u: -3.09680505839valid_h1_p_range_x.max_u: 8.72732563235valid_h1_p_range_x.mean_u: 5.48895009458valid_h1_p_range_x.min_u: 3.32030803638valid_h1_row_norms_max: 1.95904749183valid_h1_row_norms_mean: 1.40561339238valid_h1_row_norms_min: 1.16953677471valid_objective: 0.104670540623valid_y_col_norms_max: 1.93642459019valid_y_col_norms_mean: 1.90996961714valid_y_col_norms_min: 1.88659811751valid_y_max_max_class: 1.0valid_y_mean_max_class: 0.99627268242valid_y_min_max_class: 0.767024730168valid_y_misclass: 0.0122valid_y_nll: 0.0682986195071valid_y_row_norms_max: 0.536167736581valid_y_row_norms_mean: 0.38686665696valid_y_row_norms_min: 0.266996530755 Saving to mnist_pi.pkl... Saving to mnist_pi.pkl done. Time elapsed: 3.000000 seconds Time this epoch: 0:02:08.747395
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