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LeNet卷积网络",{"type":18,"tag":26,"props":419,"children":420},{},[421],{"type":18,"tag":50,"props":422,"children":424},{"alt":7,"src":423},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/b99172dfb0a043baa44ccd13d7b3ce84.png",[],{"type":18,"tag":26,"props":426,"children":427},{},[428],{"type":24,"value":429},"图7：LeNet卷积网络",{"type":18,"tag":26,"props":431,"children":432},{},[433],{"type":24,"value":434},"如上图中所示，是LeNet卷积网络的整体流程图，整体包含8个网络层，下面我们将了解每一层的计算。",{"type":18,"tag":26,"props":436,"children":437},{},[438],{"type":24,"value":439},"输入层：我们使用的数据集是MNIST数据集，该数据集中的样本数据都是规格为32×32的灰度图，我们以1个样本图片为例。那么我们输入的图片规格就是1×1×32×32，表示一个通道输入1个32×32的数组。",{"type":18,"tag":26,"props":441,"children":442},{},[443],{"type":24,"value":444},"C1层：C1层中数组规格为6×1×28×28，从1×1×32×32卷积得到。首先需要6个批次的卷积数组，每一个批次中都有1个规格为5×5的卷积数组，卷积步幅默认为1。即卷积数组规格为6×1×5×5。",{"type":18,"tag":26,"props":446,"children":447},{},[448],{"type":24,"value":449},"该卷积层共有6+1×5×5×6=156个参数，其中6个偏置参数。这一层网络**有6×1×28×28=4704个节点，每个节点和当前层5×5=25个节点相连，所以本层卷积层共有6×(1×28×28)×(1×5×5+1)=122304个全连接。",{"type":18,"tag":26,"props":451,"children":452},{},[453],{"type":24,"value":454},"S2层：S2层的数组规格为6×1×14×14，从1×1×28×28卷积得到。使用的是2×2，步幅为1的最大池化操作，所以并不改变批次数，只是将每一个输入数组从28×28降到14×14的输出数组。",{"type":18,"tag":26,"props":456,"children":457},{},[458],{"type":24,"value":459},"该池化层共有6×2=12个可训练参数，以及6×(1×14×14)×(2×2+1)=5880个全连接。",{"type":18,"tag":26,"props":461,"children":462},{},[463],{"type":24,"value":464},"C3层：C3层的数组规格为16×1×10×10，从6×1×14×14卷积得到。输出通道数数改变，所以卷积数组需要16批卷积数组，每一批中有6个卷积核与输入通道对应，每一个卷积数组规格都是5×5，步幅为1。即卷积数组规格为16×6×5×5。",{"type":18,"tag":26,"props":466,"children":467},{},[468],{"type":24,"value":469},"该卷积层共有16+1×5×5×16=2416个参数，其中16个偏置参数。这一层网络**有16×1×10×10=1600个节点，每个节点和当前层5×5=25个节点相连，所以本层卷积层共有16×(1×10×10)×(1×5×5+1)=41600个全连接。",{"type":18,"tag":26,"props":471,"children":472},{},[473],{"type":24,"value":474},"S4层：S4层的数组规格为16×1×5×5，这一层池化与S2层池化设置相同。所以输出数组只改变每一个数组的规格，不改变数量。",{"type":18,"tag":26,"props":476,"children":477},{},[478],{"type":24,"value":479},"该池化层共有16×2=32个可训练参数，以及16×(1×5×5)×(2×2+1)=2000个全连接。",{"type":18,"tag":26,"props":481,"children":482},{},[483],{"type":24,"value":484},"C5层：C5层是规格为120×1的一维向量，那么需要将S4层数组转换成一维向量，输入的数组规格是1×（16×1×5×）=1×400。使用全连接层将1×400转为1×120的向量。在全连接层中，每一个节点计算处结果后，都需要再经过激活函数计算，得出的值为输出的值。",{"type":18,"tag":26,"props":486,"children":487},{},[488],{"type":24,"value":489},"该连接层共有5×5×16=400个输入节点，参数个数为5×5×16×120+120=48120个，输出节点120个。",{"type":18,"tag":26,"props":491,"children":492},{},[493],{"type":24,"value":494},"F6层：F6层是规格为84×1的一维向量，与C5层计算相同，也是通过全连接层计算得到。为什么要转成84个神经元向量呢，如下图中所示，是所有字符标准格式，规格为12×7.所以有84个像素点，然后使用F6层的向量与这些标准图计算相似度。",{"type":18,"tag":26,"props":496,"children":497},{},[498],{"type":24,"value":499},"该连接层共有120个输入节点，参数个数为120×84+84=10164个，输出节点84个。",{"type":18,"tag":26,"props":501,"children":502},{},[503],{"type":18,"tag":50,"props":504,"children":506},{"alt":7,"src":505},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/a5dcf892a20b4ae19883b561014f9526.png",[],{"type":18,"tag":26,"props":508,"children":509},{},[510],{"type":24,"value":511},"图8：字符标准图",{"type":18,"tag":26,"props":513,"children":514},{},[515],{"type":24,"value":516},"输出层：该连接层共有84个输入节点，参数个数为84×10+10=850个，输出节点10个。",{"type":18,"tag":26,"props":518,"children":519},{},[520],{"type":24,"value":521},"输出层使用Softmax函数做多分类，在Softmax用于多分类过程中，它将多个神经元的输出，映射到（0，1）区间中，可以看作是每一个类别的概率值，从而实现多分类。Softmax从字面上来看，可以分成Soft和max两部分。Softmax的核心是Soft，对于图片分类来说，一张图片或多或少都会包含其它类别的信息，我们更期待得到图片对于每个类别的概率值，可以简单理解为每一个类别的可信度；max就是最大值的意思，选择概率值最大的当作分类的类别。",{"type":18,"tag":26,"props":523,"children":524},{},[525],{"type":24,"value":526},"下面给出Softmax函数的定义",{"type":18,"tag":26,"props":528,"children":529},{},[530],{"type":18,"tag":50,"props":531,"children":533},{"alt":7,"src":532},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/b6995881ec8f4b5ab590b4c7d32c5ad7.png",[],{"type":18,"tag":26,"props":535,"children":536},{},[537],{"type":24,"value":538},"图9：Softmax表达式",{"type":18,"tag":26,"props":540,"children":541},{},[542],{"type":24,"value":543},"其中zi是第i个节点的输出值，C是输出节点的个数，即分类类别的个数。通过Softmax函数可以将多分类的输出值转换为范围在[0，1]，并且总和为1的概率分布。当使用Softmax函数作为输出节点的激活函数的时候，一般使用交叉熵作为损失函数。模型有了损失函数后，就可以使用梯度下降的方法求解最优参数值。",{"type":18,"tag":26,"props":545,"children":546},{},[547,549],{"type":24,"value":548},"3. ",{"type":18,"tag":36,"props":550,"children":551},{},[552],{"type":24,"value":553},"交叉熵损失函数",{"type":18,"tag":26,"props":555,"children":556},{},[557],{"type":24,"value":558},"模型在项目中的职责是拟合数据的规则特性，拟合的程度我们引入损失函数表示，接下来需要定义损失函数（Loss）。损失函数是深度学习的训练目标，也叫目标函数，可以理解为神经网络的输出（Logits）和标签(Labels)之间的距离，是一个标量数据。",{"type":18,"tag":26,"props":560,"children":561},{},[562],{"type":24,"value":563},"本次模型输出是⼀个图像类别这样的离散值。对于这样的离散值预测问题，我们可以使⽤诸如softmax回归在内的分类模型。和线性回归不同，softmax回归的输出单元从⼀个变成了多个，且引⼊了softmax运算 使输出更适合离散值的预测和训练。",{"type":18,"tag":26,"props":565,"children":566},{},[567],{"type":18,"tag":50,"props":568,"children":570},{"alt":7,"src":569},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/b4417605f65f4c61b5dc44639f6731a1.png",[],{"type":18,"tag":26,"props":572,"children":573},{},[574],{"type":24,"value":575},"图10：softmax全连接运算图",{"type":18,"tag":26,"props":577,"children":578},{},[579],{"type":24,"value":580},"o1 = x1w11 + x2w21 + x3w31 + x4w41 + b1,",{"type":18,"tag":26,"props":582,"children":583},{},[584],{"type":24,"value":585},"o2 = x1w12 + x2w22 + x3w32 + x4w42 + b2,",{"type":18,"tag":26,"props":587,"children":588},{},[589],{"type":24,"value":590},"o3 = x1w13 + x2w23 + x3w33 + x4w43 + b3.",{"type":18,"tag":26,"props":592,"children":593},{},[594],{"type":24,"value":595},"既然分类问题需要得到离散的预测输出，⼀个简单的办法是将输出值oi当作预测类别是i的置信 度，并将值最⼤的输出所对应的类作为预测输出，即输出argmaxioi。然而，直接使⽤输出层的输出有两个问题。⼀⽅⾯，由于输出层的输出值的范围不确定，我们难以直观上判断这些值的意义。另⼀⽅⾯，由于真实标签是离散值，这些离散值与不确定范围的输出值之间的误差难以衡量。",{"type":18,"tag":26,"props":597,"children":598},{},[599],{"type":24,"value":600},"softmax运算符（softmax operator）解决了以上两个问题。它通过下式将输出值变换成值为正且 和为1的概率分布：",{"type":18,"tag":26,"props":602,"children":603},{},[604],{"type":18,"tag":50,"props":605,"children":607},{"alt":7,"src":606},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/613317fb63164b678baadecd4a580733.png",[],{"type":18,"tag":26,"props":609,"children":610},{},[611],{"type":24,"value":612},"图11：softmax运算符计算图",{"type":18,"tag":26,"props":614,"children":615},{},[616],{"type":24,"value":617},"容易看出yˆ1 + ˆy2 + ˆy3 = 1且0 ≤ yˆ1, yˆ2, yˆ3 ≤ 1，因此yˆ1, yˆ2, yˆ3是⼀个合法的概率分布。这时候，如 果yˆ2 = 0.8，不管yˆ1和yˆ3的值是多少，softmax运算不改变预测类别输出。",{"type":18,"tag":26,"props":619,"children":620},{},[621],{"type":24,"value":622},"使⽤softmax运算后可以更⽅便地与离散标签计算误差。我们已经知道，softmax运算 将输出变换成⼀个合法的类别预测分布。",{"type":18,"tag":26,"props":624,"children":625},{},[626],{"type":24,"value":627},"实际上，真实标签也可以⽤类别分布表达：对于样本i，我们构造向量y (i) ∈ R q ，使其第y (i)（样本i类别的离散数值）个元素为1，其余为0。这样我们的 训练⽬标可以设为使预测概率分布yˆ(i)尽可能接近真实的标签概率分布y(i)。",{"type":18,"tag":26,"props":629,"children":630},{},[631],{"type":24,"value":632},"我们可以像线性回归那样使⽤平⽅损失函数∥yˆ(i) − y (i)∥ 2/2。然而，想要预测分类结果正确，我们其实并不需要预测概率完全等于标签概率。我们只需要其中的一个预测值足够大，就足够我们分类使用。例如我们预测一个数字图片类别为“1”的预测值为0.6，预测为“7”和“9”的值为0.2，或者预测为“7”和的值为0.35，预测为“9”的值为0.05，两种情况下分类都是正确的，但是计算的损失值是不同的。改善上述问题的⼀个⽅法是使⽤更适合衡量两个概率分布差异的测量函数。其中，交叉熵（cross entropy）是⼀个常⽤的衡量⽅法。图像分类应用通常采用交叉熵损失（CrossEntropy）。",{"type":18,"tag":26,"props":634,"children":635},{},[636],{"type":18,"tag":50,"props":637,"children":639},{"alt":7,"src":638},"https://obs-mindspore-file.obs.cn-north-4.myhuaweicloud.com/file/2020/09/24/4e310e044b2648a6a114df8f782a0d13.png",[],{"type":18,"tag":26,"props":641,"children":642},{},[643],{"type":24,"value":644},"图12：交叉熵损失函数表达式",{"type":18,"tag":26,"props":646,"children":647},{},[648],{"type":24,"value":649},"其中带下标的y(i)j是向量y(i)中⾮0即1的元素，需要注意将它与样本i类别的离散数值，即不带下标的y(i)区分。在上式中，我们知道向量y (i)中只有第y(i)个元素y(i) y(i)为1，其余全为0，于是H(y (i) , yˆ (i) ) = − log yˆ(i) y(i)。也就是说，交叉熵只关⼼对正确类别的预测概率，因为只要其值⾜ 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