Is a neural network consisting of a single softmax classification layer only a linear classifier?












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$begingroup$


Since the softmax function is a generalization of the logistic function it is continuous and non-linear.



So the output of the softmax layer is: softmax( weight_matrix * input_activation)



weight_matrix * input_activation is purely linear combination of features.



The question is: if the application of the softmax activation still yields in a linear classifier or is the model then capable of representing non-linear functions?






neural-networks generalized-linear-model softmax







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    3












    $begingroup$


    Since the softmax function is a generalization of the logistic function it is continuous and non-linear.



    So the output of the softmax layer is: softmax( weight_matrix * input_activation)



    weight_matrix * input_activation is purely linear combination of features.



    The question is: if the application of the softmax activation still yields in a linear classifier or is the model then capable of representing non-linear functions?






    neural-networks generalized-linear-model softmax







    share|cite|improve this question









    $endgroup$















      3












      3








      3





      $begingroup$


      Since the softmax function is a generalization of the logistic function it is continuous and non-linear.



      So the output of the softmax layer is: softmax( weight_matrix * input_activation)



      weight_matrix * input_activation is purely linear combination of features.



      The question is: if the application of the softmax activation still yields in a linear classifier or is the model then capable of representing non-linear functions?






      neural-networks generalized-linear-model softmax







      share|cite|improve this question









      $endgroup$




      Since the softmax function is a generalization of the logistic function it is continuous and non-linear.



      So the output of the softmax layer is: softmax( weight_matrix * input_activation)



      weight_matrix * input_activation is purely linear combination of features.



      The question is: if the application of the softmax activation still yields in a linear classifier or is the model then capable of representing non-linear functions?






      neural-networks generalized-linear-model softmax




      neural-networks generalized-linear-model softmax






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Nov 22 '18 at 14:07









      tamtam_tamtam_

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          $begingroup$

          A neural network with no hidden layers and a soft max output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).



          Your explanation is right on the money: a linear combination of inputs learns linear functions, and the soft max function yields a probability vector.






          share|cite|improve this answer











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            $begingroup$

            A neural network with no hidden layers and a soft max output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).



            Your explanation is right on the money: a linear combination of inputs learns linear functions, and the soft max function yields a probability vector.






            share|cite|improve this answer











            $endgroup$


















              6












              $begingroup$

              A neural network with no hidden layers and a soft max output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).



              Your explanation is right on the money: a linear combination of inputs learns linear functions, and the soft max function yields a probability vector.






              share|cite|improve this answer











              $endgroup$
















                6












                6








                6





                $begingroup$

                A neural network with no hidden layers and a soft max output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).



                Your explanation is right on the money: a linear combination of inputs learns linear functions, and the soft max function yields a probability vector.






                share|cite|improve this answer











                $endgroup$



                A neural network with no hidden layers and a soft max output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).



                Your explanation is right on the money: a linear combination of inputs learns linear functions, and the soft max function yields a probability vector.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Nov 22 '18 at 15:36

























                answered Nov 22 '18 at 14:31









                SycoraxSycorax

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