如何在Keras的多个类别中计算总损失？

Question

假设我具有以下参数的网络：

1. 全卷积网络的语义分割
2. 损失=加权二进制交叉熵（但可以是任何损失函数，都没有关系）
3. 5类-输入是图像，地面真理是二进制掩码
4. 批次大小= 16

现在，我知道损耗是通过以下方式计算的：关于每个类别，将二进制交叉熵应用于图像中的每个像素。因此，基本上每个像素都有5个损耗值

此步骤后会发生什么？

当我训练我的网络时，它只显示一个时期的单个损失值。产生单个值需要发生许多级别的损失累积，而在文档/代码中根本不清楚如何发生。

1. 首先组合的内容-（1）该类别的损耗值（例如，每个像素组合5个值（每个类别一个）），然后是图像中的所有像素，或者（2）每个图像中的所有像素个人班级，那么所有班级的损失是加在一起的吗？
2. 这些不同的像素组合到底是如何发生的-求和在哪里/平均在哪里？
3. Keras的binary_crossentropy平均为axis=-1。那么，这是每个类别的所有像素的平均值还是所有类别的平均值，或者两者都是？

换 一种说法： 不同类别的损失如何合并以产生图像的单个损失值？

根本没有在文档中对此进行解释，无论网络类型如何，这对在keras上进行多类预测的人们都将非常有帮助。这是到keras代码开始的链接，其中第一个传递损失函数。

我能找到的最接近解释的是

loss：字符串（目标函数的名称）或目标函数。见损失。如果模型有多个输出，则可以通过传递字典或损失列表来在每个输出上使用不同的损失。该模型将使损失值最小化，将是所有单个损失的总和

来自喀拉拉邦。那么这是否意味着图像中每个类别的损失都可以简单地求和？

*此处的 *示例代码 供他人尝试。这是从Kaggle借用并针对多标签预测进行修改的基本实现：

# Build U-Net model
num_classes = 5
IMG_DIM = 256
IMG_CHAN = 3
weights = {0: 1, 1: 1, 2: 1, 3: 1, 4: 1000} #chose an extreme value just to check for any reaction
inputs = Input((IMG_DIM, IMG_DIM, IMG_CHAN))
s = Lambda(lambda x: x / 255) (inputs)

c1 = Conv2D(8, (3, 3), activation='relu', padding='same') (s)
c1 = Conv2D(8, (3, 3), activation='relu', padding='same') (c1)
p1 = MaxPooling2D((2, 2)) (c1)

c2 = Conv2D(16, (3, 3), activation='relu', padding='same') (p1)
c2 = Conv2D(16, (3, 3), activation='relu', padding='same') (c2)
p2 = MaxPooling2D((2, 2)) (c2)

c3 = Conv2D(32, (3, 3), activation='relu', padding='same') (p2)
c3 = Conv2D(32, (3, 3), activation='relu', padding='same') (c3)
p3 = MaxPooling2D((2, 2)) (c3)

c4 = Conv2D(64, (3, 3), activation='relu', padding='same') (p3)
c4 = Conv2D(64, (3, 3), activation='relu', padding='same') (c4)
p4 = MaxPooling2D(pool_size=(2, 2)) (c4)

c5 = Conv2D(128, (3, 3), activation='relu', padding='same') (p4)
c5 = Conv2D(128, (3, 3), activation='relu', padding='same') (c5)

u6 = Conv2DTranspose(64, (2, 2), strides=(2, 2), padding='same') (c5)
u6 = concatenate([u6, c4])
c6 = Conv2D(64, (3, 3), activation='relu', padding='same') (u6)
c6 = Conv2D(64, (3, 3), activation='relu', padding='same') (c6)

u7 = Conv2DTranspose(32, (2, 2), strides=(2, 2), padding='same') (c6)
u7 = concatenate([u7, c3])
c7 = Conv2D(32, (3, 3), activation='relu', padding='same') (u7)
c7 = Conv2D(32, (3, 3), activation='relu', padding='same') (c7)

u8 = Conv2DTranspose(16, (2, 2), strides=(2, 2), padding='same') (c7)
u8 = concatenate([u8, c2])
c8 = Conv2D(16, (3, 3), activation='relu', padding='same') (u8)
c8 = Conv2D(16, (3, 3), activation='relu', padding='same') (c8)

u9 = Conv2DTranspose(8, (2, 2), strides=(2, 2), padding='same') (c8)
u9 = concatenate([u9, c1], axis=3)
c9 = Conv2D(8, (3, 3), activation='relu', padding='same') (u9)
c9 = Conv2D(8, (3, 3), activation='relu', padding='same') (c9)

outputs = Conv2D(num_classes, (1, 1), activation='sigmoid') (c9)

model = Model(inputs=[inputs], outputs=[outputs])
model.compile(optimizer='adam', loss=weighted_loss(weights), metrics=[mean_iou])

def weighted_loss(weightsList):
    def lossFunc(true, pred):

        axis = -1 #if channels last 
        #axis=  1 #if channels first        
        classSelectors = K.argmax(true, axis=axis) 
        classSelectors = [K.equal(tf.cast(i, tf.int64), tf.cast(classSelectors, tf.int64)) for i in range(len(weightsList))]
        classSelectors = [K.cast(x, K.floatx()) for x in classSelectors]
        weights = [sel * w for sel,w in zip(classSelectors, weightsList)]

        weightMultiplier = weights[0]
        for i in range(1, len(weights)):
            weightMultiplier = weightMultiplier + weights[i]

        loss = BCE_loss(true, pred) - (1+dice_coef(true, pred))
        loss = loss * weightMultiplier
        return loss
    return lossFunc
model.summary()

实际的BCE-DICE损失函数可在此处找到。

问题的动机：
根据上述代码，在20个周期后，网络的总验证损失约为1％；但是，前4个班级的工会分数平均交集率均高于95％，而最后一个班级则为23％。清楚地表明5年级的学生表现不佳。但是，这种准确性上的损失根本没有反映在损失中。因此，这意味着样本的单个损失被合并在一起，从而完全抵消了我们在第五类中看到的巨大损失。而且，因此，如果将每个样本的损失分批合并，则它仍然非常低。我不确定如何协调此信息。

Answer 1

尽管我已经在相关的答案中提到了该答案的一部分，但是让我们详细地逐步检查源代码以具体找到答案。

首先，让我们前馈（！）：有一个叫于weighted_loss函数，它接受y_true，y_pred，sample_weight并mask作为输入：

weighted_loss = weighted_losses[i]
# ...
output_loss = weighted_loss(y_true, y_pred, sample_weight, mask)

weighted_loss实际上是列表的元素，该列表包含传递给fit方法的所有（增强的）损失函数：

weighted_losses = [
    weighted_masked_objective(fn) for fn in loss_functions]

我提到的“增强”一词在这里很重要。这是因为，如您在上面所看到的，实际的损失函数由另一个函数包裹，该函数weighted_masked_objective定义如下：

def weighted_masked_objective(fn):
    """Adds support for masking and sample-weighting to an objective function.
    It transforms an objective function `fn(y_true, y_pred)`
    into a sample-weighted, cost-masked objective function
    `fn(y_true, y_pred, weights, mask)`.
    # Arguments
        fn: The objective function to wrap,
            with signature `fn(y_true, y_pred)`.
    # Returns
        A function with signature `fn(y_true, y_pred, weights, mask)`.
    """
    if fn is None:
        return None

    def weighted(y_true, y_pred, weights, mask=None):
        """Wrapper function.
        # Arguments
            y_true: `y_true` argument of `fn`.
            y_pred: `y_pred` argument of `fn`.
            weights: Weights tensor.
            mask: Mask tensor.
        # Returns
            Scalar tensor.
        """
        # score_array has ndim >= 2
        score_array = fn(y_true, y_pred)
        if mask is not None:
            # Cast the mask to floatX to avoid float64 upcasting in Theano
            mask = K.cast(mask, K.floatx())
            # mask should have the same shape as score_array
            score_array *= mask
            #  the loss per batch should be proportional
            #  to the number of unmasked samples.
            score_array /= K.mean(mask)

        # apply sample weighting
        if weights is not None:
            # reduce score_array to same ndim as weight array
            ndim = K.ndim(score_array)
            weight_ndim = K.ndim(weights)
            score_array = K.mean(score_array,
                                 axis=list(range(weight_ndim, ndim)))
            score_array *= weights
            score_array /= K.mean(K.cast(K.not_equal(weights, 0), K.floatx()))
        return K.mean(score_array)
return weighted

因此，有一个嵌套函数，weighted实际上fn在line中调用了实损失函数score_array = fn(y_true, y_pred)。现在，具体来说，在提供示例的示例中，fn（即损失函数）为binary_crossentropy。因此，我们需要看一下binary_crossentropy()Keras中的定义：

def binary_crossentropy(y_true, y_pred):
    return K.mean(K.binary_crossentropy(y_true, y_pred), axis=-1)

依次调用后端函数K.binary_crossentropy()。如果使用Tensorflow作为后端，则其定义K.binary_crossentropy()如下：

def binary_crossentropy(target, output, from_logits=False):
    """Binary crossentropy between an output tensor and a target tensor.
    # Arguments
        target: A tensor with the same shape as `output`.
        output: A tensor.
        from_logits: Whether `output` is expected to be a logits tensor.
            By default, we consider that `output`
            encodes a probability distribution.
    # Returns
        A tensor.
    """
    # Note: tf.nn.sigmoid_cross_entropy_with_logits
    # expects logits, Keras expects probabilities.
    if not from_logits:
        # transform back to logits
        _epsilon = _to_tensor(epsilon(), output.dtype.base_dtype)
        output = tf.clip_by_value(output, _epsilon, 1 - _epsilon)
        output = tf.log(output / (1 - output))

    return tf.nn.sigmoid_cross_entropy_with_logits(labels=target,
                                                   logits=output)

的tf.nn.sigmoid_cross_entropy_with_logits回报：

logits与组件逻辑损失相同形状的张量。

现在，让我们backpropagate（！）：考虑以上注意事项，的输出形状K.binray_crossentropy将与y_pred（或y_true）相同。正如OP所述，y_true形状为(batch_size, img_dim, img_dim, num_classes)。因此，将K.mean(..., axis=-1)施加在形状的张量上，(batch_size, img_dim, img_dim, num_classes)这导致形状的输出张量(batch_size, img_dim, img_dim)。因此，对图像中的每个像素平均所有类别的损耗值。因此，上述score_arrayinweighted函数的形状为(batch_size, img_dim, img_dim)。还有一个步骤：weighted函数中的return语句再次取均值，即return K.mean(score_array)。那么它如何计算均值呢？如果看一下mean后端函数的定义，您会发现默认情况下该axis参数是None：

def mean(x, axis=None, keepdims=False):
    """Mean of a tensor, alongside the specified axis.
    # Arguments
        x: A tensor or variable.
        axis: A list of integer. Axes to compute the mean.
        keepdims: A boolean, whether to keep the dimensions or not.
            If `keepdims` is `False`, the rank of the tensor is reduced
            by 1 for each entry in `axis`. If `keepdims` is `True`,
            the reduced dimensions are retained with length 1.
    # Returns
        A tensor with the mean of elements of `x`.
    """
    if x.dtype.base_dtype == tf.bool:
        x = tf.cast(x, floatx())
return tf.reduce_mean(x, axis, keepdims)

然后调用tf.reduce_mean()给定axis=None参数的，对输入张量的所有轴取均值并返回一个值。因此，将(batch_size, img_dim, img_dim)计算整个形状张量的平均值，这意味着对批次中的所有标签及其所有像素取平均值，并将其作为代表损失值的单个标量值返回。然后，该损失值由Keras报告，并用于优化。

奖励：如果我们的模型具有多个输出层，因此使用了多个损失函数，该怎么办？

记住我在此答案中提到的第一段代码：

weighted_loss = weighted_losses[i]
# ...
output_loss = weighted_loss(y_true, y_pred, sample_weight, mask)

如您所见，有一个i变量用于索引数组。您可能已经猜对了：它实际上是循环的一部分，该循环使用其指定的损失函数为每个输出层计算损失值，然后取所有这些损失值的（加权）总和来计算总损失：

# Compute total loss.
total_loss = None
with K.name_scope('loss'):
    for i in range(len(self.outputs)):
        if i in skip_target_indices:
            continue
        y_true = self.targets[i]
        y_pred = self.outputs[i]
        weighted_loss = weighted_losses[i]
        sample_weight = sample_weights[i]
        mask = masks[i]
        loss_weight = loss_weights_list[i]
        with K.name_scope(self.output_names[i] + '_loss'):
            output_loss = weighted_loss(y_true, y_pred,
                                        sample_weight, mask)
        if len(self.outputs) > 1:
            self.metrics_tensors.append(output_loss)
            self.metrics_names.append(self.output_names[i] + '_loss')
        if total_loss is None:
            total_loss = loss_weight * output_loss
        else:
            total_loss += loss_weight * output_loss
    if total_loss is None:
        if not self.losses:
            raise ValueError('The model cannot be compiled '
                                'because it has no loss to optimize.')
        else:
            total_loss = 0.

    # Add regularization penalties
    # and other layer-specific losses.
    for loss_tensor in self.losses:
        total_loss += loss_tensor