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We present a derivation of the gradients of feedforward neural networks usingFr\'echet calculus which is arguably more compact than the ones usuallypresented in the literature. We first derive the gradients for ordinary neuralnetworks working on vectorial data and show how these derived formulas can beused to derive a simple and efficient algorithm for calculating a neuralnetworks gradients. Subsequently we show how our analysis generalizes to moregeneral neural network architectures including, but not limited to,convolutional networks.

A Derivation of Feedforward Neural Network Gradients Using Fr\'echet Calculus