# Back-propagation (delta rule)

Posted 2017.12.24 21:25

Back-propagation in neural network (aka delta rule)

The main intuition is to define a delta

$$\delta_k^l \equiv \frac{C}{z_k^l}$$

and find a recursive backward rule

$$\delta^l_k = \sum_m ( \delta_m^{l+1} W_{mk}^{l+1} ) \sigma'(z^l_k).$$

The gradients w.r.t. the learning parameters can be computed from the deltas.

Gradients of a convolution layer

The gradients of a convolution operation can be computed by convolution with the gradient of a loss function w.r.t. the activation and the rotated convolutional feature map.

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