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We discussed this paper in our reading group last week[0]. I think the key to understanding what's going on here is figure 1(a). The fastest learning happens with true labels, and the slowest with random labels. Shuffled pixels is the second fastest. I believe the reason this is happening is that given training data composed of structured images, the convolutional architecture heavily favors learning filters which reflect geometric features, as opposed to random filters which can memorize the data. This results in fastest learning with the true labels because the geometric features correspond to the learning target, but for memorizing random labels, geometric features have lower capacity than random filters. On the other hand, it learns shuffled pixels pretty fast because the convolutional architecture makes it easy to capture a color histogram and learn off that.

[0] This week we discussed the Alpha Go paper. URL for that, although we don't generally advertise our meetings unless we think there's going to be broad interest: https://www.meetup.com/Cambridge-Artificial-Intelligence-Mee...

I believe the reason this is happening is that given training data composed of structured images, the convolutional architecture heavily favors learning filters which reflect geometric features, as opposed to random filters which can memorize the data

And interesting idea, but you really need to test this out before assigning any particular confidence to this actually being what is happening.

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