We next explain the rationality of the resampling-by-compatibility presented in Sect. We first i) prove Eq. For Assumption (9), L( π, u, v) is strongly convex as proved in [5]. Eq. (A-19), we have E The codes are in pytorch [7]. The learning rate is 1e-5.

Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps.