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