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I wish to use a vector-valued activation function in my neural network which is injective that is, maps inputs to unique outputs. I require this property to maintain injectivity of my neural network. This has several use cases as it would make the network invertible and the resulting function that the network represents would also have properties that may be required for domain specific downstream tasks.

Are there any injective vector-valued activation functions?

Can any of the normalizations be made injective? In particular, I am using my network to evaluate a function at different x values so a normalization like layer normalization makes more sense.

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