Lab / Loss Function Explorer

Loss Function Explorer

Compare loss functions interactively. Drag predictions to see how MSE, cross-entropy, Huber, and more respond.

Click and drag to explore loss values

Show Gradients (dL/dŷ)

True value (y)1.0

Huber delta1.0

Function	Sym.	Robust	Diff.	Type	Gradient
MSE	Yes	No	Yes	Reg	Linear (grows with error)
MAE	Yes	Yes	No	Reg	Constant (always +/-1)
Huber	Yes	Yes	Yes	Reg	Linear near 0, constant for large errors

Formulas Reference

MSE: (y - ŷ)²

MAE: |y - ŷ|

Huber: ½a² if a≤δ, else δ(a-½δ)

BCE: -[y·log(p)+(1-y)·log(1-p)]

CCE: -y·log(p)

Hinge: max(0, 1-y·ŷ)

Focal: -α(1-p)ʸ·log(p)

Log-Cosh: log(cosh(y-ŷ))

Drag the vertical line or data points to explore. All computation runs entirely in your browser.