You could share the pre-trained models that take tons and tons of data and compute time to generate? The models themselves are abstract enough to be considered anonymous, by their very nature.. I think.
Take a look at the literature on de-anonymization. It's easier than you might think.
De-anonymization of data or of trained neural-nets? I've read somewhere that you can sort of 'squash' a trained net down into a simpler version for performance benefits - the caveat being that it can't do any more learning. I would think that'd make it harder to de-anonymize.
If you simplify the function, you throw away accuracy (or maybe gain, if you over-simplified). The less accurate, the harder to de-anonymize. However, you only need 32 bits of information to uniquely identify someone.