So as

[Xinfu]

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?

[Rusty]

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'.

[Xinfu]

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

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

[MWoll]

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.

[Xinfu]

Excellent answer. Thank you.