Neural Network Softmax (cross-entropy) Backpropagation Derivation Calculus












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I am trying to derive the backpropagation gradients when using softmax in the output layer with Cross-entropy Loss function. Can someone please explain why we did a Summation in the partial Derivative of Softmax below ( why not a chain rule product ) ?



enter image description here



Thanks










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$endgroup$

















    1












    $begingroup$


    I am trying to derive the backpropagation gradients when using softmax in the output layer with Cross-entropy Loss function. Can someone please explain why we did a Summation in the partial Derivative of Softmax below ( why not a chain rule product ) ?



    enter image description here



    Thanks










    share|improve this question









    New contributor




    Hamza El Bouatmani is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      I am trying to derive the backpropagation gradients when using softmax in the output layer with Cross-entropy Loss function. Can someone please explain why we did a Summation in the partial Derivative of Softmax below ( why not a chain rule product ) ?



      enter image description here



      Thanks










      share|improve this question









      New contributor




      Hamza El Bouatmani is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I am trying to derive the backpropagation gradients when using softmax in the output layer with Cross-entropy Loss function. Can someone please explain why we did a Summation in the partial Derivative of Softmax below ( why not a chain rule product ) ?



      enter image description here



      Thanks







      neural-network backpropagation math






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      Hamza El Bouatmani is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      Hamza El Bouatmani is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      edited 10 mins ago







      Hamza El Bouatmani













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      asked 2 hours ago









      Hamza El BouatmaniHamza El Bouatmani

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