What I'm talking about is indistinguishability [0], [1] which shows up in definitions of homomorphic encryption (e.g. [2], [3]). If the data is only normalized, or even encrypted in an order-preserving way, it seems possible to figure out information about the underlying data (e.g. if the target is whether a symbol moves up or down, and if you can figure out what even one of the features refer to, there's enough information to turn your model on the data into predictions you can just trade on).

[0] https://en.wikipedia.org/wiki/Computational_indistinguishabi... [1] https://en.wikipedia.org/wiki/Ciphertext_indistinguishabilit... [2] http://cs.au.dk/~stm/local-cache/gentry-thesis.pdf [3] https://arxiv.org/ftp/arxiv/papers/1305/1305.5886.pdf