i will discuss recent joint work with hayes wherein we show that any sofic group g that is initially sub-amenable (a limit of amenable groups in grigorchuk's space of marked groups) admits two embeddings into the universal sofic group s that are not conjugate by any automorphism of s. time permitting, i will also characterise precisely when two almost homomorphisms of an amenable group g are conjugate, in terms of certain irs's associated to the two actions of g. one of the applications of this is to recover the result of becker-lubotzky-thom around permutation stability for amenable groups. the main novelty of our work is the usage of von neumann algebraic techniques in a crucial way to obtain group theoretic consequences.