Have you ever thought about why neural networks are so powerful?
Why is it that no matter the task, you can find an architecture that knocks the problem out of the park?
One answer is that they can approximate any function with arbitrary precision!
Let's see how!
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From a mathematical viewpoint, machine learning is function approximation.
If you are given data points 𝑥 with observations 𝑦, learning essentially means finding a function 𝑓 such that 𝑓(𝑥) approximates the given 𝑦-s as accurately as possible.
Approximation is a very natural idea in mathematics.
Let's see a simple example!
You probably know the exponential function well. Do you also know how to calculate it?
The definition itself doesn't really help you. Calculating the powers where 𝑥 is not an integer is tough.