Forgive my ignorance, but what applications would this be used in where just maintaining copies of the initial parameters to f() wouldn’t work?
Reversibility is important in quantum computing. Quantum circuits must transform input to output in a "unitary" manner, which is reversible. If you consider the input to output as a linear transformation matrix (with complex values), then the complex conjugate of the matrix gives the "inverse function".
This is probably useless info, but reversibility in the classical sense is also interesting due to the energy bounds of computation. The Landauer limit (kTln2) [1] gives a lower bound of energy that must be dissipated to destroy one bit of information in a computation. A reversible calculation does not destroy bits.
> One of the earliest proposals to reduce heat from lost bits was to make computer circuits reversible. A reversible circuit has exactly as many outputs as inputs, assigning one output pattern to every input pattern and vice versa. That means each input can be reconstructed from the output; no bits are lost, so reversible circuits will not give off heat from bit loss. Furthermore, reversible circuits can simulate standard logic functions and can therefore be used in any computer.
[1] https://www.americanscientist.org/article/computers-that-can...
I think in the future we will see a trend of expressing most of DL model as reversible computation, with minimal irreversible module in the end and in the beginning.
Even if you only care about previous applications of f. Keeping snapshots of every input isn't always feasible.
There's as far as I can tell no inherent need to call the regular function first - given any function f, you get a callable inverse function ~f.