Binary Cross-Entropy Loss

Binary cross-entropy measures how well a model’s predicted probability matches the true 0/1 label by penalizing confident wrong answers very heavily and confident correct answers only lightly. It comes directly from the negative log-likelihood of a Bernoulli outcome, so minimizing it is equivalent to maximizing the probability assigned to the observed labels. The two terms, y log(ŷ) and (1-y) log(1-ŷ), ensure the loss only rewards the probability of the correct class and ignores the other one for each sample.

Use this loss for binary classification tasks where the model outputs a probability for one class, such as spam detection, disease screening, fraud detection, or yes/no prediction. It is the standard choice when you want probabilistic predictions and a smooth objective that works well with gradient-based optimization.

• Using predicted class labels 0/1 instead of predicted probabilities in the logarithms
• Forgetting to average over all n samples when computing the final loss
• Taking log(0) or using exact 0 and 1 probabilities without numerical clipping, which causes undefined or infinite loss