AI engineering glossary · Calculus optimisation
What is taylor series?
Taylor series: An expansion of a smooth function around a point as an infinite sum of terms built from its derivatives at that point: f(a) + f'(a)(x - a) + f''(a)(x - a)^2 / 2! + ... Truncating it gives polynomial approximations used to derive optimisers and analyse errors.
Taylor series: an example
Around 0, e^x = 1 + x + x^2/2 + x^3/6 + ..., so e^0.1 is about 1.10517 using the first four terms.
Related terms
More Calculus optimisation terms
- Total derivative
- Trust region method
- Unconstrained optimisation
- Variance reduction
- Vector-Jacobian product
- Warm restarts
- AdaGrad
- Adam
Where you learn it
Taylor series is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.