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












3














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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    3














    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?










    share|cite|improve this question

























      3












      3








      3







      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?










      share|cite|improve this question













      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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      asked Nov 22 at 14:07









      tamtam_

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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.






          share|cite|improve this answer























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            1 Answer
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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            6














            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




























              6














              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


























                6












                6








                6






                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









                Sycorax

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                38.8k1197192






























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