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I'm trying to understand the chain rule of backpropagation. This is what I understood. Is it correct?

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$$ \frac{\partial E }{ \partial w} = \sum_{i} \frac{\partial E }{ \partial a_i^{(l)} } (\sum_{j} \frac{\partial a_i^{(l)} }{ \partial a_j^{(l-1)} }(\sum_{k} \frac{\partial a_j^{(l-1)} }{ \partial a_k^{(l-2)}} \frac{\partial a_k^{(l-2)} }{ \partial z_k^{(l-2)}} \frac{\partial z_k^{(l-1)} }{ \partial w}))$$

  • $ a_i^{(l)}$ is the activation of the neuron $i$ in the $l$th layer
  • $ z_i^{(l)} $ is the sum of multiplication of weights and previous activations
  • $E$ is the error
  • $w$ is the weight
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