I want to prove that the softmax function is not invariant under scalar multiplication.
How to continue from there to prove that S(x)i is not equal to S(xc)i ?
2026-03-27 00:58:12.1774573092
How to prove that the softmax function is not invariant under scalar multiplication.
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I'll give you a direction you should follow.
Take instead the problem to solve to be that it is invariant to scalar multiplication.
A way to disprove it (i.e. that it is actually not scalar multiplication invariant) is to look at full example using a scalar of your choice (not 1 as it's not really a multiplication). (proof by contradiction to the opposite problem)