Realistically, "input is invalid" and "input is not valid" are the same. Neither is a negative frame of the other.
Typically, negative frames are not recommended, because the mind typically has to flip itself to understand the instruction. For example, "Don't think of an elephant" is an impossible instruction to follow.
In other words, you may accidentally elicit the opposite action from your user if you frame it negatively. Best to frame things positively, and with imperatives (i.e., "Do this") wherever possible.
"Don't click submit until you have filled out every field in the form" would be a silly thing to write at the top of your form. You'd probably get more people clicking submit before the form was fully filled out.
"Entry is invalid" does not tell me what I should do - it only tells me that what I did was wrong. How about: "You must enter a valid email address"
"Your password must not include the following characters: !^@$%))($" <--This may be necessary to state, but is really awful UX. It is easy to miss the "not" in that sentence. Best to let them use one and then with a validation/warning say "Your password may not include any of the following characters: !^@$%))($"
That being said, negative frames do have a place - and it usually involves inhibiting an expected action:
"Don't use the back button!"
"Do not refresh the page!"
But these MUST come with an imperative, positive statement of what to do instead. It is also good to include a reasoning behind the warning.