Your Model’s MSE Is Lying to You

Models trained with Mean Squared Error (MSE) are fundamentally misleading because they only predict the average outcome of a future event. This limitation means two models can have identical predictions and error scores, yet one might be extremely confident while the other is simply guessing—a critical distinction MSE cannot capture. For high-stakes tasks like forecasting seismic activity or grid loads, this hidden uncertainty can lead to drastically different conclusions about risk. The squared error loss function is mathematically proven to always converge on the mean of the true data distribution, actively discarding all information about the spread or variance of possible outcomes.