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SMC/particle filtering guarantees vs. VGB

Determine whether Sequential Monte Carlo and particle filtering methods for process-guided decoding can be proven to achieve theoretical guarantees comparable to Value-Guided Backtracking (VGB), such as provable coverage, mixing, or regret bounds under analogous assumptions.

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Background

The paper discusses Sequential Monte Carlo (SMC) and particle filtering approaches used for process-guided decoding, noting that they typically maintain diverse candidate sequences but do not incorporate backtracking and lack finite-time computation guarantees.

Given VGB’s provable benefits under specified assumptions, a key unresolved question is whether SMC-style methods can be endowed with comparable formal performance guarantees, bridging empirical practice and theory for process-guided sampling.

References

However, they typically do not incorporate backtracking, and lack finite-time/compute performance guarantees. It is an interesting open question whether these methods achieve comparable guarantees to VGB.

— Taming Imperfect Process Verifiers: A Sampling Perspective on Backtracking (2510.03149 - Rohatgi et al., 3 Oct 2025) in Additional Related Work, Empirical Literature—Sequential Monte Carlo and particle filtering