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CNN (convolutional neural networks) are well-known to have the nice property of "translation invariance".

Is there any other type of neural network that does not have such a property?

Or can we remove certain "layers" in CNN (such as max pooling, dropout, etc.) to "disable" translation invariance?

Possible scenarios is to:

  • classify by position (e.g. cat in the top left vs cat in the bottom right of image)

  • classified by "skewness" of object (e.g. classify squares vs rectangles).

Thanks a lot for any help.

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  • $\begingroup$ The premise of the question is false. Invariance is introduced not by convolution, but by max-pooling. $\endgroup$ Commented Oct 31, 2019 at 15:22
  • $\begingroup$ To add to the previous comment: translation invariance in CNNs with pooling layers is limited to the spatial resolution of the final convolutional layer. If your final conv layer has dimensions [5 x 5 x 128], where the first two are the spatial dimensions and the last value is the number of feature maps, then a subsequent fully-connected layer can learn to weight different spatial locations differently in a way that is not translation invariant. So unless the spatial dimensions are fully "pooled-out" before introducing FC layers, there may be some residual translation dependence. $\endgroup$ Commented Oct 31, 2019 at 17:49

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While CNNs are not completely translation invariant, common architectures are... not ideal for completing tasks where precise "positional information" is important -- for example, your example of finding the position of a cat.

CoordConv solves this with a dead simple solution: add two more channels to the input specifying the coordinate of each input pixel.

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