Improvise doesn’t change Synth Infiltrator’s mana cost or mana value, and it can’t reduce Synth Infiltrator’s cost below .

If the copied creature has in its mana cost, X is 0.

You can choose not to have Synth Infiltrator enter the battlefield as a copy of another creature. If you do, it will probably die due to having 0 toughness. (This is probably not the kind of innovation the Institute would approve of.)

If the copied creature is a token, Synth Infiltrator copies the original characteristics of that token as stated by the effect that created that token, with the noted exceptions.

If the copied creature is copying something else, then Synth Infiltrator enters the battlefield as whatever that creature copied, with the noted exceptions.

Except for being a Synth artifact creature in addition to its other types, Synth Infiltrator copies exactly what was printed on the original creature and nothing else (unless that creature is copying something else or is a token; see below). It doesn’t copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.

Any enters-the-battlefield abilities of the copied creature will trigger when Synth Infiltrator enters the battlefield. Any “as [this creature] enters the battlefield” or “[this creature] enters the battlefield with” abilities of the copied creature will also work.