AI engineering glossary · Calculus optimisation
What is lipschitz continuity?
Lipschitz continuity: A function is Lipschitz continuous with constant L if the difference in outputs is never more than L times the distance between inputs. It caps how fast the function can change and is used to bound step sizes and prove convergence.
Lipschitz continuity: an example
f(x) = 3x + 1 is Lipschitz with L = 3, since |f(a) - f(b)| = 3|a - b|.
Related terms
More Calculus optimisation terms
- Local minimum
- Loss landscape
- Mini-batch gradient descent
- Momentum
- Multivariable chain rule
- Natural logarithm
- Nesterov momentum
- Newton's method
Where you learn it
Lipschitz continuity is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.