All 'models' predicting the technological singularity are based upon, they require continual exponential growth - of intelligence, of technology, etc.
Well, if history showed anything, it showed that exponential growth in anything other than abstract mathematics is not sustainable - regardless of your attempts to 'cheat' this rule.
Technology matures and can't be improved further; etc.
IF you can keep up continual exponential growth in the AI field (and the signs are that you can't), you may - or may not (perhaps 'intelligence' in humans is a mature 'technology') - be able to have a being more intelligent than humans, functioning. But, in any case, you won't be able to keep improving that intelligence; sooner or later, you'll hit a wall.
Singularity proponents gamble that this 'wall' is beyond the singularity - and they have no convincing arguments for it.
It's almost certain there isn't a logic fundamentally 'better' than the one known to us - meaning, we have already hit the wall in this area; you may have a being thinking faster than us (quantitatively), but not qualitatively 'better'.