HackerBackpropagation, intuitively | Deep Learning Chapter 3
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A single digit calls for changes of different sizes across weights. An active input makes a weight more influential on that example; the training update has to combine the requests of many examples.
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We can't directly change those activations, we only have influence on the weights and biases.And zooming out a bit further, remember that this is all just how a single training example wishes to nudge each one of those weights and biases.