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Can someone please explain to me what a "1x1 convolution" is? I've been wondering ever since I first started reading about 1x1 convolutions a while back. My b

Can someone please explain to me what a "1x1 convolution" is? I've been wondering ever since I first started reading about 1x1 convolutions a while back. My background is not in artificial neural networks, but I understand their single neuron operation: a linear combination of inputs (optional extra input or offset), so this part behaves like any linear correlator, and then a nonlinear but typically differentiable compression sigmoid. I understand how convolutional neural networks operate, and that the synaptic weights correspond to filter kernel weights (like point spread functions, or impulse responses). Given this engineering-like interpretation I have, can someone explain to me what use convolution with a 1x1 filter has??

QuadmasterXLII 8y ago
The trick is that convolutional neural nets operate on multichannel images. Your intuition that the synaptic weights form point spread functions is correct, but you have to remember that the activation of each neuron depends on a sum of point spread functions, one for each channel in the previous layer. I like to think of 1x1 convolutions as pixel wise dense layers Here’s a toy example of a useful 1x1 convolution: you could convert a color image to greyscale by doing a 1x1 convolution with the kernel (.33, .33, .33)
- DoctorOetker 8y ago
  thank you very much, I suppose we can all agree that 1x1x3 (Width x Height x Color) convolution would have been a lot clearer. again, thanks for succinct and clear explanation!
  - daenz 8y ago
    Just to elaborate a bit more, 1x1 convolution is often used to reduce the number of parameters from the previous layer to keep the total number of parameters manageable.
    - DoctorOetker 8y ago
      yes, thank you, I understand the motivation, the reason I never understood before was quite simple, the description "1x1 convolution" (correctly) described that they were not doing convolutions across pixels. It is good to point out what they aren't doing, they should also point out what they are doing. Humor me by considering: "Today I did not go to the zoo, I did not go to school, ..., and I did not go by foot, nor by vehicle without weels, nor by a vehicle with only one wheel, nor by a vehicle that had 3 or more wheels, and the vehicle was not motorised, and I did not need to stand up on the vehicle" While true, and possibly important to point out what I didn't do, it's generally more helpful to describe what I am doing, like "I rode my bicycle to the supermarket"

QuadmasterXLII 8y ago

The trick is that convolutional neural nets operate on multichannel images. Your intuition that the synaptic weights form point spread functions is correct, but you have to remember that the activation of each neuron depends on a sum of point spread functions, one for each channel in the previous layer. I like to think of 1x1 convolutions as pixel wise dense layers Here’s a toy example of a useful 1x1 convolution: you could convert a color image to greyscale by doing a 1x1 convolution with the kernel (.33, .33, .33)

DoctorOetker 8y ago
thank you very much, I suppose we can all agree that 1x1x3 (Width x Height x Color) convolution would have been a lot clearer. again, thanks for succinct and clear explanation!
- daenz 8y ago
  Just to elaborate a bit more, 1x1 convolution is often used to reduce the number of parameters from the previous layer to keep the total number of parameters manageable.
  - DoctorOetker 8y ago
    yes, thank you, I understand the motivation, the reason I never understood before was quite simple, the description "1x1 convolution" (correctly) described that they were not doing convolutions across pixels. It is good to point out what they aren't doing, they should also point out what they are doing. Humor me by considering: "Today I did not go to the zoo, I did not go to school, ..., and I did not go by foot, nor by vehicle without weels, nor by a vehicle with only one wheel, nor by a vehicle that had 3 or more wheels, and the vehicle was not motorised, and I did not need to stand up on the vehicle" While true, and possibly important to point out what I didn't do, it's generally more helpful to describe what I am doing, like "I rode my bicycle to the supermarket"