Sound Probabilistic Safety Bounds for Large Language Models

• URL: http://arxiv.org/abs/2607.20286v1
• Date: Wed, 22 Jul 2026 15:31:28 GMT
• Title: Sound Probabilistic Safety Bounds for Large Language Models
• Abstract summary: We study a new application of the Clopper-Pearson confidence intervals to obtain probably approximately correct (PAC) bounds for this problem.<n>Our approach in particular enables the efficient computation of useful lower bounds, even in scenarios where the true harm probability is extremely small.
• Score: 50.060741829250645
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel framework for computing rigorous bounds on the probability that a large language model (LLM) generates harmful output to a given prompt. We study a new application of the Clopper-Pearson confidence intervals to obtain probably approximately correct (PAC) bounds for this problem. As our main technical contribution, we propose an algorithm that leverages features in the latent space to prioritize exploring branches in the auto-regressive generation tree that are more likely to produce harmful outputs. Our approach in particular enables the efficient computation of useful lower bounds, even in scenarios where the true harm probability is extremely small, and crucially, the obtained lower bounds are sound, i.e., formally proven to be less than the actual harmfulness probability: our experimental results demonstrate the effectiveness of our method by computing non-trivial lower bounds on state-of-the-art LLMs. This study newly enables the evaluation and statistical certification of LLMs.

Related papers

• Breaking the Computational Barrier: Provably Efficient Actor-Critic for Low-Rank MDPs [53.412166189410904]
  We use supervised learning as a computational proxy to establish a hierarchy of commonly adopted RL oracles under low-rank Markov Decision Processes (MDPs)<n>Motivated by this observation, we propose a novel optimistic actor-critic algorithm that relies solely on the policy evaluation oracle.<n>We prove that our algorithm outperforms the existing sample complexity guarantees for low-rank MDPs while avoiding computationally expensive planning or optimization oracles commonly assumed in prior works.
  arXiv  Detail & Related papers  (2026-05-02T04:46:54Z)
• BEAVER: An Efficient Deterministic LLM Verifier [11.949243456810263]
  We present BEAVER, the first practical framework for computing deterministic, sound probability bounds on large language models.<n>We formalize the verification problem, prove soundness of our approach, and evaluate BEAVER on correctness verification, privacy verification and secure code generation tasks.
  arXiv  Detail & Related papers  (2025-12-05T05:34:06Z)
• Asymptotically Optimal Linear Best Feasible Arm Identification with Fixed Budget [55.938644481736446]
  We introduce a novel algorithm for best feasible arm identification that guarantees an exponential decay in the error probability.<n>We validate our algorithm through comprehensive empirical evaluations across various problem instances with different levels of complexity.
  arXiv  Detail & Related papers  (2025-06-03T02:56:26Z)
• Assessing Correctness in LLM-Based Code Generation via Uncertainty Estimation [0.0]
  We explore uncertainty estimation as a proxy for correctness in LLM-generated code.<n>We adapt two state-of-the-art techniques from natural language generation to the domain of code generation.<n>Our findings indicate a strong correlation between the uncertainty computed through these techniques and correctness.
  arXiv  Detail & Related papers  (2025-02-17T10:03:01Z)
• Rethinking Uncertainty Estimation in Natural Language Generation [6.3398383724486544]
  Large Language Models (LLMs) are increasingly employed in real-world applications.<n>Uncertainty estimation methods generate and analyze multiple output sequences to determine the LLM's uncertainty.<n>We propose G-NLL, which has the advantage of being obtained using only a single output sequence.
  arXiv  Detail & Related papers  (2024-12-19T18:51:06Z)
• Directed Exploration in Reinforcement Learning from Linear Temporal Logic [59.707408697394534]
  Linear temporal logic (LTL) is a powerful language for task specification in reinforcement learning.<n>We show that the synthesized reward signal remains fundamentally sparse, making exploration challenging.<n>We show how better exploration can be achieved by further leveraging the specification and casting its corresponding Limit Deterministic B"uchi Automaton (LDBA) as a Markov reward process.
  arXiv  Detail & Related papers  (2024-08-18T14:25:44Z)
• Probabilistic Inference in Reinforcement Learning Done Right [37.31057328219418]
  A popular perspective in Reinforcement learning casts the problem as probabilistic inference on a graphical model of the Markov decision process (MDP) Previous approaches to approximate this quantity can be arbitrarily poor, leading to algorithms that do not implement genuine statistical inference. We first reveal that this quantity can indeed be used to generate a policy that explores efficiently, as measured by regret.
  arXiv  Detail & Related papers  (2023-11-22T10:23:14Z)
• A Learning-Based Optimal Uncertainty Quantification Method and Its Application to Ballistic Impact Problems [1.713291434132985]
  This paper concerns the optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) measure is only partially/imperfectly known. We demonstrate the learning based framework on the uncertainty optimization problem. We show that the approach can be used to construct maps for the performance certificate and safety in engineering practice.
  arXiv  Detail & Related papers  (2022-12-28T14:30:53Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Provably Efficient Reward-Agnostic Navigation with Linear Value Iteration [143.43658264904863]
  We show how iteration under a more standard notion of low inherent Bellman error, typically employed in least-square value-style algorithms, can provide strong PAC guarantees on learning a near optimal value function. We present a computationally tractable algorithm for the reward-free setting and show how it can be used to learn a near optimal policy for any (linear) reward function.
  arXiv  Detail & Related papers  (2020-08-18T04:34:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.