Existing methods typically address these issues via extensive human annotations or external supervision from more powerful models. In this work, we present a novel framework that leverages the model's self-consistency between long responses and short answers, to generate preference pairs for training. We observe that short binary questions tend to yield highly reliable responses, which can be used to query the target model to evaluate and rank its generated responses. Specifically, we design a self-reflection pipeline where detailed model responses are compared against concise binary answers, and inconsistency signals are utilized to automatically curate high-quality training data without human annotations or external model-based supervision. By relying solely on self-consistency rather than external supervision, our method offers a scalable and efficient solution that effectively reduces hallucinations using unlabeled data. Extensive experiments on multiple benchmarks, i.e., AMBER, MultiObject-Hal (ROPE), Object HalBench and MMHal-Bench, demonstrate significant improvements in factual grounding and reliability . Moreover, our approach maintains robust instruction-following ability, as evidenced by enhanced performance on LLaVA-Bench and MMBench.

Wikipedia is the largest open knowledge corpus, widely used worldwide and serving as a key resource for training large language models (LLMs) and retrieval-augmented generation (RAG) systems. Ensuring its accuracy is therefore critical. But how accurate is Wikipedia, and how can we improve it? We focus on inconsistencies, a specific type of factual inaccuracy, and introduce the task of corpus-level inconsistency detection. We present CLAIRE, an agentic system that combines LLM reasoning with retrieval to surface potentially inconsistent claims along with contextual evidence for human review. In a user study with experienced Wikipedia editors, 87.5% reported higher confidence when using CLAIRE, and participants identified 64.7% more inconsistencies in the same amount of time. Combining CLAIRE with human annotation, we contribute WIKICOLLIDE, the first benchmark of real Wikipedia inconsistencies. Using random sampling with CLAIRE-assisted analysis, we find that at least 3.3% of English Wikipedia facts contradict another fact, with inconsistencies propagating into 7.3% of FEVEROUS and 4.0% of AmbigQA examples. Benchmarking strong baselines on this dataset reveals substantial headroom: the best fully automated system achieves an AUROC of only 75.1%. Our results show that contradictions are a measurable component of Wikipedia and that LLM-based systems like CLAIRE can provide a practical tool to help editors improve knowledge consistency at scale.

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.

Recent reasoning LLMs (RLMs), especially those trained with verifier-based reinforcement learning, often perform worse with few-shot CoT than with direct answering. We revisit this paradox using high-quality reasoning traces from DeepSeek-R1 as demonstrations and find that adding more exemplars consistently degrades accuracy, even when demonstrations are optimal. A detailed analysis reveals two mechanisms behind this decline: (i) semantic misguidance, where high textual similarity leads the model to treat the target as the same as the exemplar and to copy intermediate steps verbatim; and (ii) strategy transfer failure, where the model struggles to extract useful reasoning strategies and apply them to target questions. Guided by these, we introduce Insight-to-Solve (I2S), a sequential test-time procedure that turns demonstrations into explicit, reusable insights and derives a target-specific reasoning trace; optionally, the reasoning is self-refined for coherence and correctness (I2S+). Extensive experiments on diverse benchmarks show that I2S and I2S+ consistently outperform both direct answering and test-time scaling baselines across open- and closed-source models. Even for GPT models, our method helps: on AIME'25, GPT-4.1 rises by +14.0%, and o1-mini improves by +2.7% on AIME and +1.7% on GPQA, indicating that in-context demonstrations can be harnessed effectively via insight-refine-solve framework.

Large Language Models (LLMs) have achieved impressive performance across diverse tasks but continue to struggle with learning transitive relations, a cornerstone for complex planning. To address this issue, we investigate the Multi-Token Prediction (MTP) paradigm and its impact to transitive relation learning. We theoretically analyze the MTP paradigm using a Transformer architecture composed of a shared output head and a transfer layer. Our analysis reveals that the transfer layer gradually learns the multi-step adjacency information, which in turn enables the backbone model to capture unobserved transitive reachability relations beyond those directly present in the training data, albeit with some inevitable noise in adjacency estimation. Building on this foundation, we propose two strategies to enhance the transfer layer and overall learning quality: Next-Token Injection (NTI) and a Transformer-based transfer layer. Our experiments on both synthetic graphs and the Blocksworld planning benchmark validate our theoretical findings and demonstrate that the improvements significantly enhance the model's path-planning capability. These findings deepen our understanding of how Transformers with MTP learn in complex planning tasks, and provide practical strategies to overcome the transitivity bottleneck, paving the way toward structurally aware and general-purpose planning models.

Test-time entropy minimization helps adapt a model to novel environments and incentivize its reasoning capability, unleashing the model's potential during inference by allowing it to evolve and improve in real-time using its own predictions, achieving promising performance. However, pure entropy minimization can favor non-generalizable shortcuts, such as inflating the logit norm and driving all predictions to a dominant class to reduce entropy, risking collapsed solutions (e.g., constant one-hot outputs) that trivially minimize the objective without meaningful learning. In this paper, we introduce ZeroSiam, an efficient asymmetric Siamese architecture tailored for test-time entropy minimization. ZeroSiam prevents collapse through asymmetric divergence alignment, which is efficiently achieved by a learnable predictor and a stop-gradient operator before the classifier. We provide empirical and theoretical evidence that ZeroSiam not only prevents collapse solutions, but also absorbs and regularizes biased learning signals, enhancing performance even when no collapse occurs. Despite its simplicity, extensive results show that ZeroSiam performs more stably over prior methods using negligible overhead, demonstrating efficacy on both vision adaptation and large language model reasoning tasks across challenging test scenarios and diverse models, including tiny models that are particularly collapse-prone.

The transformer architecture introduced by [V aswani et al., 2017] has demonstrated capabilities across a wide range of tasks [Liu et al., 2018, Devlin et al., 2019, Rad-ford et al., 2019, Touvron et al., 2023, OpenAI, 2023], showing particularly significant progress in logical reasoning. These models can not only solve complex mathematical problems Davies et al. [2021] but have also reached performance levels comparable to top human contestants in the International Mathematical Olympiad (IMO) [Trinh et al., 2024]. The reasoning capabilities of large language models are fundamentally shaped by the thinking strategies they employ.

Large Language Models (LLMs) employ multi-turn interaction as a fundamental paradigm for completing complex tasks. However, their performance often degrades in extended interactions, as they are typically trained on static, single-turn data, which hinders their ability to adapt to real-time user feedback. To address this limitation, we first propose a new paradigm: Test-Time Policy Adaptation for Multi-Turn Interactions (T2PAM), which utilizes user feedback from the ongoing interaction as a reward signal to estimate a latent optimal policy aligned with user preferences, then updates a small subset of parameters to steer the model toward this policy, ultimately enabling efficient in-conversation self-correction. We then introduce Optimum-Referenced One-Step Adaptation (ROSA), a lightweight algorithm that operationalizes T2PAM. ROSA guides the model parameters toward a theoretical optimal policy in a single, efficient update step, avoiding costly iterative gradient-based optimization and minimizing computational overhead. We provide a rigorous theoretical analysis guaranteeing that the policy of ROSA converges to the preference of user as the number of interactions increases. Extensive experiments on challenging benchmark demonstrate that ROSA achieves significant improvements in both task effectiveness and efficiency.

Test-time scaling via solution sampling and aggregation has become a key paradigm for improving the reasoning performance of Large Language Models (LLMs). While reward model selection is commonly employed in this approach, it often fails to identify minority-yet-correct answers, which limits its effectiveness beyond that of simple majority voting. We argue that this limitation stems from a lack of informative critique signals during verifier training. To bridge this gap, we introduce Mirror-Critique, a framework that trains a verifier with informative critiques. Our key insight is to leverage the rich critique signal by contrasting model-generated solutions with ground-truth solutions. We deploy a small instruction-tuned model to synthesize high-quality critique data with rejection sampling that teaches the verifier not only what is wrong, but also why. The synthetic data is used to cold-start the LLMs in the RL VR process to further improve the verification ability. The resulting Mirror-V erifier is deployed to evaluate candidate solutions by generating multiple critiques per solution, aggregating them into a verify score used for weighted voting or selective abstention. The experimental results show that our Mirror-V erifier significantly outperforms majority voting in terms of solution accuracy and also improves the solver's honesty to recognize and abstain from answering beyond its capability boundaries. Reinforcement Learning with V erifiable Reward (RL VR) has emerged as a powerful method for training Large Language Models (LLMs) to perform complex reasoning tasks, enabling significant improvements in domains such as mathematics, code generation, and scientific problem-solving.

Tree search has recently emerged as a powerful framework for aligning generative models with task-specific rewards at test time. Applying tree search to Masked Diffusion Language Models, however, introduces two key challenges: (i) parallel unmasking yields highly correlated branches, limiting exploration, and (ii) reward evaluation via sampled completions produces high-variance estimates, making pruning unstable. Theoretically, we quantify branching efficiency gains in NFEs (number of function evaluations), show that the scoring rule approximates the true reward with error bounded by predictive uncertainty, and prove improvements with larger tree widths. Masked Diffusion Language Models (MDLMs) (Nie et al., 2025; Sahoo et al., 2024; Shi et al., 2024; Y ang et al., 2025b) have emerged as a compelling alternative to autoregressive models (Brown et al., 2020; Radford et al., 2019; Touvron et al., 2023). They start with all-mask tokens and gradually reveal tokens through a sequence of discrete denoising steps. At each step, the model predicts token distributions for masked positions, conditioned on the current partially masked sequence and the diffusion timestep. This formulation enables flexible sampling schedules and broad conditioning patterns, making MDLMs well-suited for controllable generation tasks.Figure 1: Conceptual illustration of TR However, this flexibility is not fully realized without mechanisms to align the model's outputs with user-defined objectives. Test-Time Alignment (TT A) enables guiding language model outputs toward task-specific goals without retraining. In applications such as toxicity avoidance (Logacheva et al., 2022), sentiment control (Barbieri et al., 2020), or enforcing linguistic acceptability (Warstadt et al., 2019), aligning generation with external reward functions at test time offers a flexible and training-free alternative to supervised fine-tuning.