What does “permutation invariant” mean in the context of neural networks doing image recognition?

I have seen a term “permutation invariant” version of the MNIST digit recognition task. What does it mean?

Answer

In this context this refers to the fact that the model does not assume any spatial relationships between the features. E.g. for multilayer perceptron, you can permute the pixels and the performance would be the same. This is not the case for convolutional networks, which assume neighbourhood relations.

Attribution
Source : Link , Question Author : RockTheStar , Answer Author : bayerj

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