# Binary Cross-Entropy Loss

Binary Cross-Entropy loss is a special case of Cross-Entropy loss used for multilabel classification (taggers). It is the cross entropy loss when there are only two classes involved. It is reliant on Sigmoid activation functions.

Mathematically, it is given as,

$BinaryC.E=-\sum_i^2 t_i log\left(p_i\right)$

Where $€€t_i€€$ is the true label and $€€p_i€€$ is the probability of the $€€i^\left\{th\right\}€€$ label.

python
      # importing the library
import torch
import torch.nn as nn

# Binary Cross-Entropy Loss

target = torch.ones([10, 64], dtype=torch.float32)  # 64 classes, batch size = 10
output = torch.full([10, 64], 1.5)  # A prediction (logit)

pos_weight = torch.ones([64])  # All weights are equal to 1
criterion = torch.nn.BCEWithLogitsLoss(pos_weight=pos_weight)
criterion(output, target)  # -log(sigmoid(1.5))

python
      # importing the library
import tensorflow as tf

y_true = [[0., 1.], [0., 0.]]
y_pred = [[0.6, 0.4], [0.4, 0.6]]

# Using 'auto'/'sum_over_batch_size' reduction type.
bce = tf.keras.losses.BinaryCrossentropy()
bce(y_true, y_pred).numpy()

# Calling with 'sample_weight'.
bce(y_true, y_pred, sample_weight=[1, 0]).numpy()