The key limitation of the verification performance lies in the ability of error detection. With this intuition we designed several variants of pessimistic verification, which are simple workflows that could significantly improve the verification of open-ended math questions. In pessimistic verification we construct multiple parallel verifications for the same proof, and the proof is deemed incorrect if any one of them reports an error. This simple technique significantly improves the performance across many math verification benchmarks without incurring substantial computational resources. Its token efficiency even surpassed extended long-CoT in test-time scaling. Our case studies further indicate that the majority of false negatives in stronger models are actually caused by annotation errors in the original dataset, so our method's performance is in fact underestimated. Self-verification for mathematical problems can effectively improve the reliability and performance of language model outputs, and it also plays a critical role in enabling long-horizon mathematical tasks. We believe that research on pessimistic verification will help enhance the mathematical capabilities of language models across a wide range of tasks.

A challenge in human-AI decision-making is to balance three factors: the correctness of predictions, the cost of knowledge and reasoning complexity, and the confidence about whether to abstain from automated answers or escalate to human experts. In this work, we present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise -- a base model for initial candidate answers, a more capable and knowledgeable (but costlier) large model, and a human expert for when the model cascade abstains. Our method proceeds in two stages. First, a deferral policy determines whether to accept the base model's answer or regenerate it with the large model based on the confidence score. Second, an abstention policy decides whether the cascade model response is sufficiently certain or requires human intervention. Moreover, to overcome static policies and accommodate changing task difficulty, we incorporate an online learning mechanism which uses human feedback. We demonstrate this approach to general question-answering (ARC-Easy, ARC-Challenge, and MMLU) and medical question-answering (MedQA and MedMCQA). Our results demonstrate that our cascaded strategy outperforms single-model baselines in most cases, achieving higher accuracy while reducing costs and providing a principled approach to handling abstentions.

Empirical scaling laws establish a relationship between the number of parameters and model capability, as evidenced by models with hundreds of billions of parameters achieving state-of-the-art results on benchmarks (Kaplan et al., 2020; Grattafiori et al., 2024). However, the autoregressive generation process requires accessing all model parameters for each forward pass, creating a memory bandwidth bottleneck that impacts token generation latency. Furthermore, current trends toward more sophisticated LLM applications, such as multi-hop reasoning (Wei et al., 2022), tool integration (Patil et al., 2024), and reasoning capability (Y ang et al., 2025; DeepMind, 2025), produce longer output sequences, amplifying the computational burden of inference. One prominent approach to address inference latency is Speculative Decoding (SD), which achieves partial parallelization of the generation process (Leviathan et al., 2023; Chen et al., 2023). Standard SD operates by deploying a computationally efficient draft model to propose candidate token sequences, which are subsequently validated in parallel by the target model (the model of interest). The acceptance criterion for draft tokens relies on a probability-based alignment verification: draft tokens are accepted when their likelihood under the target model meets or exceeds their likelihood under the draft model.

With respect to improving the reasoning accuracy of LLMs, the representative reinforcement learning (RL) method GRPO faces failure due to insignificant reward variance, while verification methods based on process reward models (PRMs) suffer from difficulties with training data acquisition and verification effectiveness. To tackle these problems, this paper introduces ReST-RL, a unified LLM RL paradigm that significantly improves LLM's code reasoning ability by combining an improved GRPO algorithm with a meticulously designed test time decoding method assisted by a value model (VM). As the first stage of policy reinforcement, ReST-GRPO adopts an optimized ReST algorithm to filter and assemble high-value training data, increasing the reward variance of GRPO sampling, thus improving the effectiveness and efficiency of training. After the basic reasoning ability of LLM policy has been improved, we further propose a test time decoding optimization method called VM-MCTS. Through Monte-Carlo Tree Search (MCTS), we collect accurate value targets with no annotation required, on which VM training is based. When decoding, the VM is deployed by an adapted MCTS algorithm to provide precise process signals as well as verification scores, assisting the LLM policy to achieve high reasoning accuracy. We conduct extensive experiments on coding problems to verify the validity of the proposed RL paradigm. Upon comparison, our approach significantly outperforms other reinforcement training baselines (e.g., naive GRPO and ReST-DPO), as well as decoding and verification baselines (e.g., PRM-BoN and ORM-MCTS) on well-known coding benchmarks of various levels (e.g., APPS, BigCodeBench, and HumanEval), indicating its power to strengthen the reasoning ability of LLM policies. Codes for our project can be found at https://github.com/THUDM/ReST-RL.

Image-based AI models are increasingly deployed across a wide range of domains, including healthcare, security, and consumer applications. However, many image datasets carry sensitive or proprietary content, raising critical concerns about unauthorized data usage. Data owners therefore need reliable mechanisms to verify whether their proprietary data has been misused to train third-party models. Existing solutions, such as backdoor watermarking and membership inference, face inherent trade-offs between verification effectiveness and preservation of data integrity. In this work, we propose HoneyImage, a novel method for dataset ownership verification in image recognition models. HoneyImage selectively modifies a small number of hard samples to embed imperceptible yet verifiable traces, enabling reliable ownership verification while maintaining dataset integrity. Extensive experiments across four benchmark datasets and multiple model architectures show that HoneyImage consistently achieves strong verification accuracy with minimal impact on downstream performance while maintaining imperceptible. The proposed HoneyImage method could provide data owners with a practical mechanism to protect ownership over valuable image datasets, encouraging safe sharing and unlocking the full transformative potential of data-driven AI.

With growing demands for privacy protection, security, and legal compliance (e.g., GDPR), machine unlearning has emerged as a critical technique for ensuring the controllability and regulatory alignment of machine learning models. However, a fundamental challenge in this field lies in effectively verifying whether unlearning operations have been successfully and thoroughly executed. Despite a growing body of work on unlearning techniques, verification methodologies remain comparatively underexplored and often fragmented. Existing approaches lack a unified taxonomy and a systematic framework for evaluation. To bridge this gap, this paper presents the first structured survey of machine unlearning verification methods. We propose a taxonomy that organizes current techniques into two principal categories -- behavioral verification and parametric verification -- based on the type of evidence used to assess unlearning fidelity. We examine representative methods within each category, analyze their underlying assumptions, strengths, and limitations, and identify potential vulnerabilities in practical deployment. In closing, we articulate a set of open problems in current verification research, aiming to provide a foundation for developing more robust, efficient, and theoretically grounded unlearning verification mechanisms.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). To support this approach, we construct a high-quality instruction-following dataset, VerInstruct, containing approximately 22,000 instances with associated verification signals. We apply RL training with VerIF to two models, achieving significant improvements across several representative instruction-following benchmarks. The trained models reach state-of-the-art performance among models of comparable size and generalize well to unseen constraints. We further observe that their general capabilities remain unaffected, suggesting that RL with VerIF can be integrated into existing RL recipes to enhance overall model performance. We have released our datasets, codes, and models to facilitate future research at https://github.com/THU-KEG/VerIF.

Conformal Prediction (CP) has proven to be an effective post-hoc method for improving the trustworthiness of neural networks by providing prediction sets with finite-sample guarantees. However, under adversarial attacks, classical conformal guarantees do not hold anymore: this problem is addressed in the field of Robust Conformal Prediction. Several methods have been proposed to provide robust CP sets with guarantees under adversarial perturbations, but, for large scale problems, these sets are either too large or the methods are too computationally demanding to be deployed in real life scenarios. In this work, we propose a new method that leverages Lipschitz-bounded networks to precisely and efficiently estimate robust CP sets. When combined with a 1-Lipschitz robust network, we demonstrate that our lip-rcp method outperforms state-of-the-art results in both the size of the robust CP sets and computational efficiency in medium and large-scale scenarios such as ImageNet. Taking a different angle, we also study vanilla CP under attack, and derive new worst-case coverage bounds of vanilla CP sets, which are valid simultaneously for all adversarial attack levels. Our lip-rcp method makes this second approach as efficient as vanilla CP while also allowing robustness guarantees.

The synergistic mechanism based on Speculative Decoding (SD) has garnered considerable attention as a simple yet effective approach for accelerating the inference of large language models (LLMs). Nonetheless, the high rejection rates require repeated LLMs calls to validate draft tokens, undermining the overall efficiency gain of SD. In this work, we revisit existing verification mechanisms and propose a novel synergetic mechanism Consultant Decoding (CD). Unlike SD, which relies on a metric derived from importance sampling for verification, CD verifies candidate drafts using token-level likelihoods computed solely by the LLM. CD achieves up to a 2.5-fold increase in inference speed compared to the target model, while maintaining comparable generation quality (around 100% of the target model's performance). Interestingly, this is achieved by combining models whose parameter sizes differ by two orders of magnitude. In addition, CD reduces the call frequency of the large target model to below 10%, particularly in more demanding tasks. CD's performance was even found to surpass that of the large target model, which theoretically represents the upper bound for speculative decoding.

Large language models (LLMs) suffer from high inference latency due to the auto-regressive decoding process. Speculative decoding accelerates inference by generating multiple draft tokens using a lightweight model and verifying them in parallel. However, existing verification methods rely heavily on distributional consistency while overlooking semantic correctness, thereby limiting the potential speedup of speculative decoding. While some methods employ additional models for relaxed verification of draft tokens, they often fail to generalize effectively to more diverse or open-domain settings. In this work, we propose Reflective Verification, a training-free and semantics-aware approach that achieves a better trade-off between correctness and efficiency. Specifically, we leverage the inherent reflective capacity of LLMs to semantically assess the correctness of draft tokens in parallel during verification. Using prompt-based probing, we obtain both the original and reflective distributions of draft tokens in a single forward pass. The fusion of these distributions enables semantic-level verification of draft tokens that incorporates both consistency and correctness. Experiments across multiple domain benchmarks and model scales demonstrate that our method significantly increases the acceptance length of draft tokens without compromising model performance. Furthermore, we find that the proposed Reflective Verification is orthogonal to existing statistical verification methods, and their combination yields additional 5$\sim$15\% improvements in decoding speed.