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I read somewhere that a Multilayer Perceptron is a recursive function in its forward propagation phase. I am not sure, what is the recursive part? For me, I would see a MLP as a chained function. So, it would nice anyone could relate a MLP to a recursive function.

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Inherently, no. The MLP is just a data structure. It represents a function, but a standard MLP is just representing an input-output mapping, and there's no recursive structure to it.

On the other hand, possibly your source is referring to the common algorithms that operate over MLPs, specifically forward propagation for prediction and back propagation for training. Both of these algorithms are easy to think about recursively, with each node performing a sort of recursive call with its children or parents as the target, and some useful information about activations or errors attached. I actually encourage my students to implement it recursively for this reason, even though it's probably not the most efficient solution.

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Sure, you can define plenty of things we don't generally need to regard as recursive as so. An MLP is just a series of functions applied to its input. This can be loosely formulated as

$$ o_n = f(o_{n-1})$$

Where $o_n$ is the output of layer $n$.

But this clearly doesn't reveal, much does it?

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