Focal Loss is widely used in object detection to address class imbalance, but its theoretical roots are often glossed over. This post takes a step back and derives Focal Loss from information theory, specifically from the concept of self-information. The key insight is that Focal Loss can be seen as a cross-entropy loss where each sample's contribution is weighted by a function of its predicted probability, effectively reducing the influence of well-classified examples. The derivation starts from the definition of information content and shows how the modulating factor (1 - pt)^gamma naturally arises. This perspective not only clarifies why Focal Loss works but also opens the door to designing new loss functions based on information-theoretic principles. For engineers and researchers, understanding this foundation can lead to better hyperparameter tuning and more principled model improvements. The post is concise but mathematically rigorous, making it a valuable reference for anyone working with imbalanced datasets.
This post derives Focal Loss from first principles using information theory, showing how it naturally emerges as a weighted cross-entropy that down-weights easy examples. It provides a deeper theoretical foundation for practitioners who use Focal Loss in object detection and classification tasks.