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I was reading chapter 2 of Michael Nielsen's book on deep learning: enter image description here

Shouldn't the circle word read "forward" instead of "backward" because we are using the weighted inptut to layer l?

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No, as the previous sentence, with "backward" italicized states, a measure of the error is moving from layer $l + 1$ back to layer $l$. This is reducing the layer index, i.e., going backwards among the numbered activation layers.

This section of text is, as the title states, discussing Backpropagation which is an important aspect giving a lot of the power of artificial neural networks and deep learning.

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