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?
neural-networks generalized-linear-model softmax
asked Nov 22 at 14:07
tamtam_
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up vote
3
down vote
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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?
neural-networks generalized-linear-model softmax
asked Nov 22 at 14:07
tamtam_
363
add a comment |
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
asked Nov 22 at 14:07
tamtam_
363
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
asked Nov 22 at 14:07
tamtam_
363
asked Nov 22 at 14:07
tamtam_
363
asked Nov 22 at 14:07
tamtam_
363
asked Nov 22 at 14:07
tamtam_
363
asked Nov 22 at 14:07
tamtam_
363
363
add a comment |
add a comment |
1 Answer
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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.
answered Nov 22 at 14:31
Sycorax
38.2k997186
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 22 at 14:31
Sycorax
38.2k997186
add a comment |
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.
answered Nov 22 at 14:31
Sycorax
38.2k997186
add a comment |
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.
answered Nov 22 at 14:31
Sycorax
38.2k997186
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.
answered Nov 22 at 14:31
Sycorax
38.2k997186
edited Nov 22 at 15:36
answered Nov 22 at 14:31
Sycorax
38.2k997186
answered Nov 22 at 14:31
Sycorax
38.2k997186
answered Nov 22 at 14:31
Sycorax
38.2k997186
38.2k997186
add a comment |
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