I trained a CNN w/o pooling on MNIST and produced a colored visualization of the feature maps you get when you translate a digit on an input canvas. This illustrates the equivariance property of convolutions. More info (why convolutions?) in a blog post: medium.com/@chriswolfvision/…

Oct 5, 2020 · 10:12 AM UTC

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GIF
Replying to @chriswolfvision
That's awesome! What did you use to create the animation?
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Thanks :) All done by hand, ~500 lines of PyTorch, but only ~250 lines are the visualization code, the rest is standard boiler plate code for model training and validation. I considered using libraries like pyrender, but found this quicker (4h of coding Sunday afternoon).
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Replying to @chriswolfvision
Even fully convolutional layers without pooling aren't translation equivariant, they can and will encode position information: "On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location" arxiv.org/abs/2003.07064

On Translation Invariance in CNNs: Convolutional Layers can...

In this paper we challenge the common assumption that convolutional layers in modern CNNs are translation invariant. We show that CNNs can and will exploit the absolute spatial location by...

arxiv.org
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Yes, through boundary effects, forgot to mention that. Thanks.
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Replying to @chriswolfvision @CSProfKGD
Beautiful animation, and I am looking forward to reading your blog post. Looks like gold!
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Replying to @chriswolfvision
Problem comes when using strides :/
Replying to @chriswolfvision
We do very similar visualisations to analyse the equivariance of our segmentation algorithms.
Replying to @chriswolfvision
equivariance to translation, right? does it equivariance to rotation as well?
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