[imurray]

I'm sceptical about the energy motivation, but there are multiple reasons why making invertible deep learning architectures can be interesting or useful. Cf, a series of workshops from 2019-2021: https://invertibleworkshop.github.io/

Since then diffusion models have been popular. Generating from these can be seen as a special case of a continuous time normalizing flow, and so (in theory) is a reversible computation. Although the distilled/fast generation that's run in production is probably not that!

Simulating differential equations is not usually actually reversible in practice due to round-off errors. But when done carefully, simulations performed in a computer can actually be exactly bit-for-bit reversible: https://arxiv.org/abs/1704.07715

[imurray]

Another machine learning paper ("ancient", 2015) where being able to exactly reverse a computation was useful: https://arxiv.org/abs/1502.03492