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Bootstrap Flow-Map-Tree (a.k.a BFMT), a computationally efficient sampling framework that enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling.
It is proved that the resulting sampling framework yields a multi-particle interaction-aware Feynman-Kac corrector that progressively steers the multi-particle system toward a KL-tilted target distribution, facilitating global exploration and preventing mode collapse.
A reconstruction-driven design density is derived and the posterior mean is used to build a training-free warp that places more measurements where the target function varies rapidly, and a geometric equalizer separately corrects boundary bias.
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