I agree, there’s nothing specific to neural network activations here. In particular, the visual intuition that if you translate the two datasets until they have the same mean (which is weaker than mean ablation), you will have a hard time finding a good linear classifier, doesn’t rely on the shape of the data.
But it’s not trivial or generally true either: the paper I linked to give some counterexamples of datasets where mean ablation doesn’t prevent you from building a classifier with >50% accuracy. The rough idea is that the mean is weak to outliers, but outliers don’t matter if you want to produce high-accuracy classifiers. Therefore, what you want is something like the median.
I agree, there’s nothing specific to neural network activations here. In particular, the visual intuition that if you translate the two datasets until they have the same mean (which is weaker than mean ablation), you will have a hard time finding a good linear classifier, doesn’t rely on the shape of the data.
But it’s not trivial or generally true either: the paper I linked to give some counterexamples of datasets where mean ablation doesn’t prevent you from building a classifier with >50% accuracy. The rough idea is that the mean is weak to outliers, but outliers don’t matter if you want to produce high-accuracy classifiers. Therefore, what you want is something like the median.