If the singularity mind was bigger than us, but of the same nature, we would be able to compute it with pencil and paper, or in a computer, and to analyze it to see how it works (very slowly, as a Turing machine).
My impression is that we couldn't, just like we couldn't decode an audio file that stream forever without real-time decoding. Once we "compute it" "very slowly," the AI will already have improved twice, tenfold, a thousandfold. It will be fruitless.
Not to mention, even if the AI is simply a Von Neumann machine with really impressive specs, what makes you think we'd be able to decode it? If you gave me a RAM chip, I wouldn't know what to do with it without an EE book. Now imagine a technology a thousand times more advanced.