The induction of the AR method ensures that the order of appended operator 'batch' in P th iteration, {e θ 1,P T1 , e θ 2,P T2 , ..., e θ κ P ,P Tκ P }, containing κ P operators, is apposite. Consequently, the final Ansätze generated by AR-AAs should be as compact as the one generated by original counterparts, with a quicker convergence guaranteed.