Let a Neural network is trained. Let multiple number of inputs result same output. We can determine any one input for a particular output using neural network. But, how can we determine all the inputs for a given output. To be precise, Let, x+y=10. So for 10 the inputs are (1,9),(2,8),(3,7) and so on.
You can’t. Even for $x+y=10$ there’s infinitely many possible inputs. You can pick random $x$, say $526149.6427855$ and solve for $y$
$$ 526149.6427855 - 10 = y $$
same can be done for any $x$, or for any $y$.
Neutral networks are deterministic, but much more complicated then summation, so solving it wouldn’t be that simple. Moreover, they almost always have multiple inputs, for example you input $32\times 32 \times 3$ image and get single number as output, or for recurrent neutral network, you take a sequence of any length, possibility infinite, and get a number, so that’s much harder then two unknowns. Neural networks also use many non-linear and wasteful transformations, e.g. ReLU activation transforms any $x<0$ to zero, MaxPool takes many different values and returns single, highest one, etc., so there’s many inputs that lead to their output. Even finding a single input that might have produced the given output of neutral network is non-trivial problem, since its seeking for a needle in a haystack, not talking about finding all such inputs.