Loss Function Explorer
Every loss is an opinion about error: MSE panics at outliers, MAE counts calmly, log-loss fears confident mistakes.
Tip: park the error at zero, drop the outlier, and watch the three means disagree.
Try this
- Run the panic test. Error at zero, then drop the +4.5 outlier: MSE leaps past 10 while MAE strolls to 2.25. Same data, different fears — the legend narrates it.
- Find Huber's hinge. Slide the error slowly from 0 to 3 and watch the mint curve: parabola until 1, straight line after. The kink at δ is the compromise made visible.
- Price certainty. Flip to classification with truth y = 1: push p to 0.99 and note the tiny bill — then drag to 0.01 and feel the explosion. Confidence cuts both ways.
How to read a loss
In regression, MSE squares each error — big misses dominate, so one outlier can shout down a hundred good predictions. MAE takes absolute values instead: every unit of error costs the same, outliers included. Huber splits the difference, quadratic near zero and linear beyond δ = 1.
In classification, log-loss charges −ln(probability of the truth): confident and right is nearly free, confident and wrong is catastrophic — far steeper than the dashed linear penalty beside it. That acceleration near certainty is why classifiers learn humility.
Training makes sense once you've priced an error
This explorer is one small piece of how ManySpace teaches machine learning — every idea as something you can slide, drop, and compare.