So as

So as
 

Is my sentence correct?

-Our __ has to match the sound __ the words in our memory, so as translators do.

Space 1: brain (not brains)
Space 2: with (not to)

What do you think about my choice?

Your choice for 'space 1' is correct, since it agrees with the verb.
I like your choice for 'space 2', as well (but some people like to use 'to').

The stuff you highlighted in red should not begin with 'so'.

Thank you, but then how should I rewrite it, if it's wrong?

I would write:
"Our brain has to match the sound to the words in our memory, like translators do."

But "with the words" and "as translators do" are also correct.

Excellent answer. Thank you.