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Cross Entropy vs MSE: Which Loss Function Should You Use?

Loss functions play a pivotal role in training machine learning models. They quantify how well a model’s predictions align with the actual data, providing the essential feedback signal needed for learning. Two of the most widely used loss functions in supervised learning are Mean Squared Error (MSE) and Cross Entropy. This comprehensive guide explores their mathematical underpinnings, practical applications, differences in optimization behavior, and best practices for choosing between them.

A loss function (or cost function) measures the discrepancy between the model's predictions and the actual values. During training, machine learning algorithms adjust their parameters to minimize this loss, thereby improving prediction accuracy.

Selecting the right loss function is crucial as it directly influences the learning dynamics and the final performance of your model.