Finally, we use hard EM, as it has been found to yield better models than the standard soft EM on a number of different task (e.g., (Johnson, 2007)).
instead of standard 'soft' EM updates with phrase counts weighted according to the posterior P (z = i| e, f ), we use the 'winner-takes-all' approach: Here,ẑ e, f is the "winning" latent subdomain for sentence pair e, f : In practice, we found that using this hard version leads to better performance.