1x1 convolutions, equivalence with fully connected layer
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I'm confused by the concept of equating a 1x1 convolution with a fully connected layer. Take the following simple example of a 1x1 convolution of 2 input channels each of size 2x2, and a single output channel.
The only way I can relate this to fully connected layers is to say that there are 4 fully connected layers, one for each location in the input feature map (inputs and outputs colour coded).
From what I can understand my interpretation is consistent with the Network in Network paper[Lin et al. 2013] which describe the 1x1 as being equivalent as cross channel parametric pooling
The cross channel parametric pooling layer is also equivalent to a
convolution layer with 1x1 con- volution kernel.
I have seen
this one from Yann LeCunn equating 1x1 convolutions to a fully connected layer. And I have read this answer and I'm just not seeing the equivalence between a 1x1 convolution over an input volume and a single fully connected layer...
Any insight would be appreciated, if you can please relate back to the example above. Thanks!
neural-network convnet
asked 18 hours ago
nixonnixon
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I'm confused by the concept of equating a 1x1 convolution with a fully connected layer. Take the following simple example of a 1x1 convolution of 2 input channels each of size 2x2, and a single output channel.
The only way I can relate this to fully connected layers is to say that there are 4 fully connected layers, one for each location in the input feature map (inputs and outputs colour coded).
From what I can understand my interpretation is consistent with the Network in Network paper[Lin et al. 2013] which describe the 1x1 as being equivalent as cross channel parametric pooling
The cross channel parametric pooling layer is also equivalent to a
convolution layer with 1x1 con- volution kernel.
I have seen
this one from Yann LeCunn equating 1x1 convolutions to a fully connected layer. And I have read this answer and I'm just not seeing the equivalence between a 1x1 convolution over an input volume and a single fully connected layer...
Any insight would be appreciated, if you can please relate back to the example above. Thanks!
neural-network convnet
asked 18 hours ago
nixonnixon
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm confused by the concept of equating a 1x1 convolution with a fully connected layer. Take the following simple example of a 1x1 convolution of 2 input channels each of size 2x2, and a single output channel.
The only way I can relate this to fully connected layers is to say that there are 4 fully connected layers, one for each location in the input feature map (inputs and outputs colour coded).
From what I can understand my interpretation is consistent with the Network in Network paper[Lin et al. 2013] which describe the 1x1 as being equivalent as cross channel parametric pooling
The cross channel parametric pooling layer is also equivalent to a
convolution layer with 1x1 con- volution kernel.
I have seen
this one from Yann LeCunn equating 1x1 convolutions to a fully connected layer. And I have read this answer and I'm just not seeing the equivalence between a 1x1 convolution over an input volume and a single fully connected layer...
Any insight would be appreciated, if you can please relate back to the example above. Thanks!
neural-network convnet
asked 18 hours ago
nixonnixon
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm confused by the concept of equating a 1x1 convolution with a fully connected layer. Take the following simple example of a 1x1 convolution of 2 input channels each of size 2x2, and a single output channel.
The only way I can relate this to fully connected layers is to say that there are 4 fully connected layers, one for each location in the input feature map (inputs and outputs colour coded).
From what I can understand my interpretation is consistent with the Network in Network paper[Lin et al. 2013] which describe the 1x1 as being equivalent as cross channel parametric pooling
The cross channel parametric pooling layer is also equivalent to a
convolution layer with 1x1 con- volution kernel.
I have seen
this one from Yann LeCunn equating 1x1 convolutions to a fully connected layer. And I have read this answer and I'm just not seeing the equivalence between a 1x1 convolution over an input volume and a single fully connected layer...
Any insight would be appreciated, if you can please relate back to the example above. Thanks!
neural-network convnet
neural-network convnet
asked 18 hours ago
nixonnixon
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
nixonnixon
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
nixonnixon
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 18 hours ago
nixonnixon
1112
asked 18 hours ago
nixonnixon
1112
1112
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
nixon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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