Efficient Theoretical Guarantees for FALCON Likelihood Accuracy

Establish an efficient theoretical guarantee that the likelihood estimates produced by FALCON’s few-step invertible flow maps are correct for self-normalized importance sampling in Boltzmann Generation, ensuring the estimates’ theoretical validity without incurring prohibitive computational cost.

Background

FALCON enables few-step sampling with likelihoods accurate enough for importance sampling in practice by training invertible flow maps with a hybrid objective. While empirical performance is strong across multiple molecular systems, the authors note that they lack an efficient theoretical guarantee of correctness for the computed likelihoods.

Obtaining such guarantees would strengthen the theoretical foundation of FALCON as a Boltzmann Generator, ensuring that its fast likelihood evaluations are not only empirically accurate but also provably correct under reasonable assumptions and computational budgets.