喀拉斯邦不同批次大小的损失计算 [英] loss calculation over different batch sizes in keras

问题描述

我知道，从理论上讲，一批网络的损失只是所有单个损失的总和.这反映在 Keras代码计算总损失.相关:

I know that in theory, the loss of a network over a batch is just the sum of all the individual losses. This is reflected in the Keras code for calculating total loss. Relevantly:

            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

但是，我注意到，当我训练一个带有batch_size=32和batch_size=64的网络时，每个时期的损耗值仍然或多或少地相同，只是差额为~0.05%.但是，两个网络的准确性都完全相同.因此，从本质上讲，批量大小对网络没有太大影响.

However, I noticed that when I train a network with a batch_size=32 and a batch_size=64, the loss value for every epoch still comes out to more or less the same with only a ~0.05% difference. However, the accuracy for both networks remained the exact same. So essentially, the batch size didn't have too much effect on the network.

我的问题是，当我将批次数量加倍时，假设损失确实在被累加，损失不应该实际上是先前价值的两倍，或者至少更大吗?准确度保持完全相同的事实，否定了网络可能通过更大的批量学习得更好的借口.

My question is when I double the batch size, assuming the loss is really being summed, shouldn't the loss in fact be double the value it was previously, or at least greater? The excuse that the network probably learned better with the bigger batch size is negated by the fact the accuracy has stayed exactly the same.

无论批次大小如何，损失大致保持不变的事实使我认为这是平均水平.

The fact that the loss stays more or less the same regardless of the batch size makes me think it's being averaged.

推荐答案

您发布的代码涉及多输出模型，其中每个输出可能都有自己的损失和权重.因此，将不同输出层的损耗值相加.但是，您可以在

The code you have posted concerns multi-output models where each output may have its own loss and weights. Hence, the loss values of different output layers are summed together. However, The individual losses are averaged over the batch as you can see in the losses.py file. For example this is the code related to binary cross-entropy loss:

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

更新:在添加了此答案的第二部分(即损失函数)之后，作为OP，我对损失函数定义中的axis=-1感到困惑，我想我本人必须用axis=0表示批次中的平均值?！然后我意识到，对于由多个单元组成的输出层，在损耗函数的定义中使用的所有K.mean()都存在.那么，该批次的平均损失在哪里?我检查了代码以找到答案:获取特定损失函数的损失值，

Update: Right after adding the second part of the this answer (i.e. loss functions), as the OP, I was baffled by the axis=-1 in the definition of loss function and I thought to myself that it must be axis=0 to indicate the average over the batch?! Then I realized that all the K.mean() used in the definition of loss function are there for the case of an output layer consisting of multiple units. So where is the loss averaged over the batch? I inspected the code to find the answer: to get the loss value for a specific loss function, a function is called taking the true and predicted labels as well as the sample weights and mask as its inputs:

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

此weighted_losses[i]功能是什么?您可能会发现，这是一个元素(增强的)损失函数列表:

what is this weighted_losses[i] function? As you may find, it is an element of list of (augmented) loss functions:

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

fn实际上是 losses.py 文件，也可以是用户定义的自定义损失函数.现在，这个weighted_masked_objective函数是什么?它已在 training_utils.py 文件:

fn is actually one of the loss functions defined in losses.py file or it may be a user-defined custom loss function. And now what is this weighted_masked_objective function? It has been defined in training_utils.py file:

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

如您所见，首先在行score_array = fn(y_true, y_pred)中计算每个样本损失，然后最后返回损失的平均值，即return K.mean(score_array).因此可以确认所报告的损失是每批次中每个样本损失的平均值.

As you can see, first the per sample loss is computed in the line score_array = fn(y_true, y_pred) and then at the end the average of the losses is returned, i.e. return K.mean(score_array). So that confirms that the reported losses are the average of per sample losses in each batch.

请注意，如果使用Tensorflow作为后端，则K.mean() 调用 tf.reduce_mean()函数.现在，当在没有axis参数的情况下调用K.mean()时(axis参数的默认值为None)，如在weighted_masked_objective函数中调用的那样，相应的对tf.reduce_mean() 计算所有轴上的均值并返回一个单一值.这就是为什么无论输出层的形状和所使用的损失函数如何，Keras都只使用和报告单个损失值的原因(应该这样，因为优化算法需要最小化标量值，而不是矢量或张量)

Note that K.mean(), in case of using Tensorflow as backend, calls the tf.reduce_mean() function. Now, when K.mean() is called without an axis argument (the default value of axis argument would be None), as it is called in weighted_masked_objective function, the corresponding call to tf.reduce_mean() computes the mean over all the axes and returns one single value. That's why no matter the shape of output layer and the loss function used, only one single loss value is used and reported by Keras (and it should be like this, because optimization algorithms need to minimize a scalar value, not a vector or tensor).

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