It is possible for some non-linear autoencoder to compress the input data into the same dimension as PCA but can preserve more information than PCA does?
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Yes, imagine that your data points lie on a circle. PCA projection down to 1 dimension will position points on opposite sides of the circle next to each other, whereas non-linear projection down to 1 dimension can avoid this problem to some extent (though local neighborhood structure cannot be preserved at the end-points).
Auto-encoders are a broad class of models, so some auto-encoders can do the right thing here but not all. For instance, here's an autoencoder architecture that would not do better than PCA: https://arxiv.org/pdf/1804.10253.pdf
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