chainer.functions.softmax_cross_entropy(x, t, normalize=True, cache_score=True, class_weight=None, ignore_label=- 1, reduce='mean', enable_double_backprop=False, soft_target_loss='cross-entropy')[source]

Computes cross entropy loss for pre-softmax activations.

  • x (Variable or N-dimensional array) – Variable holding a multidimensional array whose element indicates unnormalized log probability: the first axis of the variable represents the number of samples, and the second axis represents the number of classes. While this function computes a usual softmax cross entropy if the number of dimensions is equal to 2, it computes a cross entropy of the replicated softmax if the number of dimensions is greater than 2.

  • t (Variable or N-dimensional array) – Variable holding a signed integer vector of ground truth labels. If t[i] == ignore_label, corresponding x[i] is ignored. When the dtype is float, this function treats t as an array holding probability distribution of labels, in other words, soft targets. In this case, the shape of t must be the same as the shape of x. Note that the loss is calculated using cross entropy or KL divergence.

  • normalize (bool) – If True, this function normalizes the cross entropy loss across all instances. If False, it only normalizes along a batch size.

  • cache_score (bool) – When it is True, the function stores result of forward computation to use it on backward computation. It reduces computational cost though consumes more memory. If enable_double_backprop option is True, this option is forcibly turned off and the function does not cache the intermediate value.

  • class_weight (N-dimensional array) – An array that contains constant weights that will be multiplied with the loss values along with the second dimension. The shape of this array should be (x.shape[1],). If this is not None, each class weight class_weight[i] is actually multiplied to y[:, i] that is the corresponding log-softmax output of x and has the same shape as x before calculating the actual loss value.

  • ignore_label (int) – Label value you want to ignore. Its default value is -1. See description of the argument t.

  • reduce (str) – A string that determines whether to reduce the loss values. If it is 'mean', it computes the sum of the individual cross entropy and normalize it according to normalize option. If it is 'no', this function computes cross entropy for each instance and does not normalize it (normalize option is ignored). In this case, the loss value of the ignored instance, which has ignore_label as its target value, is set to 0.

  • enable_double_backprop (bool) – If True, this function uses implementation that supports higher order differentiation. If False, it uses single-backprop implementation. This function use the single-backprop version because we expect it is faster. So, if you need second or higher derivatives, you need to turn it on explicitly.

  • soft_target_loss (str) – A string that determines what type of method is used to calculate soft target loss. If 'cross-entropy' and 'kl-divergence', cross-entropy and KL divergence are used for loss calculation.


A variable holding a scalar array of the cross entropy loss. If reduce is 'mean', it is a scalar array. If reduce is 'no', the shape is same as that of t.

Return type



This function is differentiable only by x.


>>> x = np.array([[-1, 0, 1, 2], [2, 0, 1, -1]]).astype(np.float32)
>>> x
array([[-1.,  0.,  1.,  2.],
       [ 2.,  0.,  1., -1.]], dtype=float32)
>>> t = np.array([3, 0]).astype(np.int32)
>>> t
array([3, 0], dtype=int32)
>>> y = F.softmax_cross_entropy(x, t)
>>> y
>>> log_softmax = -F.log_softmax(x)
>>> expected_loss = np.mean([log_softmax[row, column].data for row, column in enumerate(t)])
>>> y.array == expected_loss