Rare-Event Estimation

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Rare-event estimation seeks reliable probabilities for outcomes that occur too infrequently for ordinary Monte Carlo sampling, such as system failures, climate extremes, unsafe language-model outputs, or molecular transitions. Common approaches include importance sampling, subset simulation and multilevel splitting, cross-entropy methods, and sequential Monte Carlo; newer methods use learned or generative proposals to steer samples toward relevant outcomes. These techniques can reduce the number of simulations needed, but their usefulness depends on finding the important event regions while keeping estimates unbiased and variance manageable. A continuing challenge is validating estimates when events are extremely rare and results depend on model calibration, proposal quality, or the distribution of inputs being evaluated.

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29 papers6 papers in the last four weeks, up 20% on the four weeks before. 0.0% of all new papers.

Amplify, Locate, Estimate (ALE) on Rare-Failure Rates of Fine-Tuned LLMs
Oct 26, 2026Patrick Reichherzer, Jonathan Evertz, Thorsten HolzRare-Event Estimation Language Model Safety Evaluation
Max Planck Institute for Security and Privacy (MPI-SP) · CISPA Helmholtz Center for Information Security
Learned Control Variates for Rare Grid-Outage Estimation at Electric Vehicle Charging Stations
Oct 19, 2026Sulyman Iyanda, Mansur AriefRare-Event Estimation Variance Reduction
Industrial and Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Rarity of Singletons Matters & Supplementary Materials
Oct 15, 2026Pragatheeswaran Vipulanandan, Kamal Premaratne, Dilip SarkarRare-Event Estimation Robust Estimation
Dept. of Elect. and Comp. Engineering University of Miami Coral Gables, FL 33146, USA · Dept. of Comp. Science University of Miami Coral Gables, FL 33146, USA
Weighted Ensemble Sampling for Rare-Event Estimation in Language Models
Oct 13, 2026Zixuan Liu, Gustavo Didier, Fangzheng Wu +2Rare-Event Estimation LLM Reliability
Department of Computer Science, Tulane University, New Orleans, LA, 70118, USA · Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA
Estimating Uncoded Crash Factors with Tabular Foundation and System One Models: Kumo Tabular and Jev
Oct 7, 2026Amir Rafe, Subasish DasRare-Event Estimation Tabular Foundation Models
Texas State University, San Marcos, USA
Steering Diffusion Models to Rare Events with Sequential Monte Carlo
Oct 6, 2026Aavash Subedi, Tim Reichelt, Christopher Williams +3Diffusion Model Sampling Importance Sampling
Department of Statistics, University of Oxford · Department of Physics, University of Oxford · Department of Statistics, University of British Columbia
Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures
Oct 5, 2026Paweł Lorek, Rafał Nowak, Rafał Topolnicki +2Gaussian Mixture Models Importance Sampling
University of Wrocław · Tooploox · TRAILS University of Warsaw +3
Quantifying Behavioral Tails in Black-Box Language Models
Sep 27, 2026Elsayed Eshra, Ali Al-Lawati, Dongwon Lee +1Language Model Safety Evaluation LLM Safety
The Pennsylvania State University University Park, PA 16802, USA
A Free Knob: Decoupling Calibration and Predictive Skill in Threshold-Based Evaluation
Sep 27, 2026Md Tanveer Hossain Munim, Bijoy Ahmed Saiem, Al-Amin Sany +1Post-Hoc Calibration Probability Calibration
Regional Integrated Multi-Hazard Early Warning System (RIMES) · Bangladesh University of Engineering and Technology (BUET)
Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
Sep 25, 2026Isabella S. Thiel, Juan Bello-Rivas, Yannis G. Kevrekidis +1Rare-Event Estimation Chaotic Time-Series Prediction
Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139 · Department of Applied Mathematics and Statistics, Johns Hopkins University Baltimore, MD 21218 · Department of Chemical and Biomolecular Engineering, Johns Hopkins University Baltimore, MD 21218
Rare Event Estimation via Iterative Unalignment
Sep 21, 2026Hanming Yang, Daksh Mittal, Jing Dong +1Importance Sampling LLM Safety
Decision, Risk, and Operations Division, Columbia Business School
Neural noise enables accurate internal simulation of rare events
Sep 16, 2026Heng Zhang, Pawel Herman, Zenas C. ChaoComputational Cognitive Modeling Rare-Event Estimation
International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Japan · Division of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden
Scale-invariant Optimal Sampling for Rare-events Data with Sparse Models
Aug 23, 2026Jing Wang, HaiYing Wang, Qiang Zhang +1Rare-Event Estimation Adaptive Sampling
Department of Statistics, University of Connecticut, Storrs, CT 06269, USA · Vickie and Jack Farber Vision Research Center, Wills Eye Hospital Thomas Jefferson University, 840 Walnut St, Philadelphia, PA 19107, USA · Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Adaptive Multilevel Twisted Sequential Monte Carlo for Rare Events Estimation in Language Models
Aug 22, 2026Zixuan Liu, Fangzheng Wu, Brian Summa +1Rare-Event Estimation Language Model Safety Evaluation
Department of Computer Science, Tulane University, New Orleans, LA, 70118, USA
Interpretable Causal Discovery via Causal-Effect Constraints
Aug 12, 2026Cixuan Zhang, Guy Van den Broeck, Benjie WangBayesian Inference Causal Discovery
Computer Science Dept., Yale University, New Haven, Connecticut, USA · Computer Science Dept., University of California, Los Angeles, Los Angeles, California, USA
Estimating Rare Events in Language Models with Proper Evaluation
Jul 20, 2026Nikita Y. Parulekar, Anqi LiuLanguage Model Safety Evaluation Proper Scoring Rules
Johns Hopkins University
Diachronic Sample Integration: Robust Tail-Risk Estimation with Generative Models
Jul 12, 2026Shuning Zhao, Patrick Wong, Leran Zhang +1Ensemble Learning Generative Modeling
Department of Computer Science and Technology, BNRist, Tsinghua University, China · Department of Econometrics and Business Statistics, Monash Business School, Monash University, Australia · School of Mathematics and Statistics, University of Melbourne, Australia
SCARCE: Scalable Cascade Analysis for Rare-event Characterisation via Embeddings
Jun 28, 2026Yingjie Wang, Yi Dong, Edmund Lau +3LLM Safety Evaluation Rare-Event Estimation
University of Liverpool, UK · UK AI Security Institute, UK · Loughborough University, UK +1
Quantum enhanced rare event discovery and sampling
Jun 4, 2026Naixu Guo, Po-Wei Huang, Qisheng Wang +4Heavy-Tailed Distributions Rare-Event Estimation
Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore · Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom · School of Computer Science, Shanghai Jiao Tong University, Shanghai 200240, China +4
Scalable Counterfactual Risk Estimation for Rare Events in Longitudinal Data
Jun 1, 2026Xiaohui Yin, Avijit Mitra, Ying Zhou +2Causal Effect Estimation Survival Analysis
University of Massachusetts Amherst Amherst, Massachusetts, USA · University of Massachusetts Lowell Lowell, Massachusetts, USA
Measuring Five-Nines Reliability: Sample-Efficient LLM Evaluation in Saturated Benchmarks
May 11, 2026Eungyeup Kim, Chenchen Gu, Vashisth Tiwari +1LLM Evaluation LLM Reliability
Carnegie Mellon University
Estimating the expected output of wide random MLPs more efficiently than sampling
May 6, 2026Wilson Wu, Victor Lecomte, Michael Winer +3Multilayer Perceptrons Efficient Inference
Alignment Research Center
Towards accurate extreme event likelihoods from diffusion model climate emulators
May 5, 2026Peter Manshausen, Noah Brenowitz, Julius Berner +2Diffusion Model Guidance Climate Science
NVIDIA, Santa Clara, CA, USA
Estimating Tail Risks in Language Model Output Distributions
Apr 24, 2026Rico Angell, Raghav Singhal, Zachary Horvitz +4Language Model Safety Evaluation Importance Sampling
Center for Data Science, New York University · Department of Computer Science, New York University · Columbia University
Rare Event Analysis via Stochastic Optimal Control
Apr 14, 2026Yuanqi Du, Jiajun He, Dinghuai Zhang +2Rare-Event Estimation Stochastic Optimal Control
Microsoft Research New England · Cornell University · University of Cambridge +1
Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models
Apr 10, 2026Shuo-Hui Li, Chen Chen, Yao-Wen Zhang +1Free Energy Calculation Rare-Event Estimation
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China · Department of Chemistry, The Hong Kong University of Science and Technology, Hong Kong, China · IAS Center for AI for Scientific Discoveries, Hong Kong University of Science and Technology, Hong Kong, China
Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis
Mar 10, 2026Alexis KirkeRare-Event Estimation
Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Models
Feb 18, 2026Yu Xie, Ludwig Winkler, Lixin Sun +10Free Energy Calculation Diffusion Sampling
Microsoft Research AI for Science
Reasoning-Enhanced Rare-Event Prediction with Balanced Outcome Correction
Jan 23, 2026Vitaly Bulgakov, Alexander TurchinClass-Imbalanced Learning Rare-Event Prediction
Mass General Brigham, Boston, MA, USA · Profiteya LLC, Boston, MA, USA

Oct 26, 2026J/K move · Enter open · S save

Amplify, Locate, Estimate (ALE) on Rare-Failure Rates of Fine-Tuned LLMs

Patrick Reichherzer, Jonathan Evertz, Thorsten Holz

Max Planck Institute for Security and Privacy (MPI-SP) · CISPA Helmholtz Center for Information Security

Rare-Event Estimation Language Model Safety Evaluation Safety-Preserving Fine-Tuning of Language Models

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Safety fine-tuning can make undesirable model behaviors sufficiently rare that measuring their frequency by direct sampling becomes prohibitively expensive. We introduce Amplify, Locate, Estimate (ALE), a method for estimating such rare failure probabilities efficiently. ALE uses the change in token log-probabilities induced by the safety fine-tuning to define an amplification direction, along which we increase the failure rate for cheap measurement. We develop a score-function estimator that uses the selected amplified batch to recover the local slope of the log failure rate from the token probabilities of the sampled failures, enabling extrapolation back to rare target rates. We also use the amplified batch to obtain an importance-sampling estimate. Across 41 evaluation targets, ALE's estimate-to-reference ratios have a median close to one, with 37 ALE estimates within a factor of three of reference values obtained from independent direct measurements. Ablation tests show that with a budget of up to

\sim

1000 labeled rollouts, in addition to a cheap unlabeled scan, ALE estimates failure probabilities for Qwen3-8B fine-tunes down to about

10^{-5}

, where direct measurement can require hundreds of thousands of rollouts, as the required sampling budget scales inversely with failure probability at fixed relative precision.