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












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?










share|cite|improve this question









$endgroup$

















    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?










    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?










      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






      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_

      363




      363






















          1 Answer
          1






          active

          oldest

          votes


















          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











          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "65"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f378276%2fis-a-neural-network-consisting-of-a-single-softmax-classification-layer-only-a-l%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            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












              $begingroup$

              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

                41.9k12109206




                41.9k12109206






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Cross Validated!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f378276%2fis-a-neural-network-consisting-of-a-single-softmax-classification-layer-only-a-l%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    這個網誌中的熱門文章

                    Xamarin.form Move up view when keyboard appear

                    Post-Redirect-Get with Spring WebFlux and Thymeleaf

                    Anylogic : not able to use stopDelay()