# Adaptive Multilevel Twisted Sequential Monte Carlo for Rare Events Estimation in Language Models

arXiv: https://arxiv.org/abs/2608.21736 · HTML: https://mlsanity.com/paper/2608.21736/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Secrets of RLHF in Large Language Models Part II: Reward Modeling](https://mlsanity.com/paper/2401.06080/) (2024)
- [Explore, Establish, Exploit: Red Teaming Language Models from Scratch](https://mlsanity.com/paper/2306.09442/) (2023)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [DisasterResponseGPT: Large Language Models for Accelerated Plan of Action Development in Disaster Response Scenarios](https://mlsanity.com/paper/2306.17271/) (2023)
- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [Forecasting Rare Language Model Behaviors](https://mlsanity.com/paper/2502.16797/) (2025)
- [A Baseline Analysis of Reward Models' Ability To Accurately Analyze Foundation Models Under Distribution Shift](https://mlsanity.com/paper/2311.14743/) (2023)
- [From Prompts to Protection: Large Language Model-Enabled In-Context Learning for Smart Public Safety UAV](https://mlsanity.com/paper/2506.02649/) (2025)
- [Estimating Tail Risks in Language Model Output Distributions](https://mlsanity.com/paper/2604.22167/) (2026)
- [Rare Event Analysis of Large Language Models](https://mlsanity.com/paper/2602.06791/) (2026)
- [Inference-Time Alignment of Diffusion Models via Trust-Region Iterative Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2605.25123/) (2026)
- [Improving Constrained Language Generation via Self-Distilled Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2507.02315/) (2025)
- [LatticeBridge: Rare-Event Sequential Inference for Faithful Structured Sequence Synthesis](https://mlsanity.com/paper/2606.11203/) (2026)

## Built on by (most cited first, 2 of 2)

- [Quantifying Behavioral Tails in Black-Box Language Models](https://mlsanity.com/paper/2609.33638/) (2026)
- [Estimating Great Expectations Under Autoregressive Language Models with Potentials](https://mlsanity.com/paper/2610.11399/) (2026)

## Abstract (arXiv)

Rare unsafe behaviors in large language models can remain practically significant even when their probability is extremely small, particularly at deployment scales involving millions or billions of interactions. Twisted Sequential Monte Carlo (SMC) provides a principled framework for rare-event probability estimation by learning twist functions that guide generation toward a target event. However, the standard twist learning framework relies on positive samples from the rare-event target distribution, which may be nearly absent before an informative twist has been learned, resulting in unreliable rare-event estimation. We propose Adaptive Multilevel Twisted SMC, which learns the rare-event twist through a sequence of progressively rarer intermediate events. At each level, the learned twist provides more informative positive examples for learning the next twist, ultimately leading to a more accurate final twist for the target rare event. Experiments across diverse tasks and model scales show that the proposed method produces more accurate rare-event probability estimates. By enabling more reliable discovery of hard-to-observe unsafe behaviors, our method provides a practical tool for strengthening the evaluation and safety alignment of deployed language models.