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Aren't feed-forward neural networks just a bunch of transformation matrices transforming vectors?

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I am a newbie at neural networks and I was learning about good ol' simple feed-forward neural networks.

Am I right in saying that going from one layer to the next, is essentially just transforming a vector with some transformation matrix and then applying an activation function to the resulting vector?

Or am I missing some crucial piece of understanding regarding neural networks?

submitted by SunTzusWetDream
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