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





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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?






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    up vote
    3
    down vote

    favorite












    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







    New contributor




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






















      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      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







      New contributor




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











      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







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      tamtam_ is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      asked Nov 22 at 14:07









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          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.






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            up vote
            6
            down vote













            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



























              up vote
              6
              down vote













              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

























                up vote
                6
                down vote










                up vote
                6
                down vote









                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














                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 at 15:36

























                answered Nov 22 at 14:31









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