This research paper investigates Sequential Monte Carlo (SMC) and other particle filtering algorithms as a theoretical framework for improving large language model (LLM) inference. The authors introduce a principled approach to analyze inference-time interventions, such as parallel reasoning and pruning, by utilizing process reward models to steer generation. Their findings establish non-asymptotic guarantees for SMC based on criteria like bounded action-level coverage and divergence between true and approximate reward distributions. To address limitations in standard SMC, they propose SMC with Rejection Sampling (SMC-RS), which maintains high accuracy even when reward models are nearly perfect. Empirically, the study demonstrates that SMC consistently outperforms Best-of-N sampling on complex mathematical reasoning tasks and benchmarks. Ultimately, the work bridges the gap between ad hoc sampling heuristics and rigorous statistical theory to optimize the accuracy-cost tradeoff in AI inference.