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How do we measure when one probability distribution fails to match another? 📊 KL divergence quantifies the information lost when approximating distribution P with Q. It's the foundation of: → Neural network training (cross-entropy loss) → Variational autoencoders (VAEs) → Knowledge distillation → Policy optimization in RL The key insight: it's asymmetric. Forward KL is mean-seeking, reverse KL is mode-seeking.
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