In the past, CIPSI calculations were only possible in practice thanks to approximations. e rst approximation restricts the set A n by de ning a set of generators. Indeed, it is very unlikely that |α will be selected if it is not connected to any |I with a large coe cient, so only the determinants with the largest coe cients are generators. A second approximation de nes a set of selectors in order to reduce the cost of e α by removing the determinants with the smallest coecients in the expression of Ψ (0) in E . is approximate scheme was introduced in the 80's and is known as threeclass CIPSI. e downside of these approximations is that the calculation is biased and, consequently, does not strictly converge to the FCI limit. Moreover, similar to the initiator approximation in FCIQMC, this scheme su ers from a sizeconsistency issue. e stochastic selection that we describe in this section (asymptotically) cures this problem, as there is no threshold on the wave function: if the calculation is run long enough, the unbiased FCI solution is obtained.