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Can LLMs Learn to Reason Robustly under Noisy Supervision?

arXiv:2604.03993v1 Announce Type: cross Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In this work, we take the first step toward a systematic analysis of noisy label mechanisms in RLVR. In contrast to supervised classification, most RLVR algorithms incorporate a rollout-based condition: a label's influence on training is contingent on whether the current policy can generate rollouts that realize it, a property that naturally extends to noisy labels. Based on this observation, we distinguish two types of noise: inactive noisy labels, which reduce data efficiency, and active noisy labels, which are reinforced and risk skewing the model toward incorrect distributions. From experiments on training with noisy samples, we identify an Early Correctness Coherence phenomenon: although noisy samples begin to lag behind in later stages, accuracy on both clean and noisy samples increases similarly in early training. Motivated by this dynamic, we propose Online Label Refinement (OLR), which progressively corrects potentially noisy labels with majority-voted answers when two conditions hold: a positive slope in the majority answer's rollout pass rate and stable historical consistency across updates, enabling gradual self-correction as the policy improves. We evaluate OLR on six in-distribution mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). Across noise ratios from 0.1 to 0.9, OLR consistently improves robustness under both inactive and active noisy-label settings, achieving average gains of 3.6% to 3.9% on in-distribution benchmarks and 3.3% to 4.6% on out-of-distribution evaluations.

Combating Data Laundering in LLM Training

arXiv:2604.01904v1 Announce Type: cross Abstract: Data rights owners can detect unauthorized data use in large language model (LLM) training by querying with proprietary samples. Often, superior performance (e.g., higher confidence or lower loss) on a sample relative to the untrained data implies it was part of the training corpus, as LLMs tend to perform better on data they have seen during training. However, this detection becomes fragile under data laundering, a practice of transforming the stylistic form of proprietary data, while preserving critical information to obfuscate data provenance. When an LLM is trained exclusively on such laundered variants, it no longer performs better on originals, erasing the signals that standard detections rely on. We counter this by inferring the unknown laundering transformation from black-box access to the target LLM and, via an auxiliary LLM, synthesizing queries that mimic the laundered data, even if rights owners have only the originals. As the search space of finding true laundering transformations is infinite, we abstract such a process into a high-level transformation goal (e.g., "lyrical rewriting") and concrete details (e.g., "with vivid imagery"), and introduce synthesis data reversion (SDR) that instantiates this abstraction. SDR first identifies the most probable goal for synthesis to narrow the search; it then iteratively refines details so that synthesized queries gradually elicit stronger detection signals from the target LLM. Evaluated on the MIMIR benchmark against diverse laundering practices and target LLM families (Pythia, Llama2, and Falcon), SDR consistently strengthens data misuse detection, providing a practical countermeasure to data laundering.

Beyond In-Domain Detection: SpikeScore for Cross-Domain Hallucination Detection

arXiv:2601.19245v4 Announce Type: replace Abstract: Hallucination detection is critical for deploying large language models (LLMs) in real-world applications. Existing hallucination detection methods achieve strong performance when the training and test data come from the same domain, but they suffer from poor cross-domain generalization. In this paper, we study an important yet overlooked problem, termed generalizable hallucination detection (GHD), which aims to train hallucination detectors on data from a single domain while ensuring robust performance across diverse related domains. In studying GHD, we simulate multi-turn dialogues following LLMs' initial response and observe an interesting phenomenon: hallucination-initiated multi-turn dialogues universally exhibit larger uncertainty fluctuations than factual ones across different domains. Based on the phenomenon, we propose a new score SpikeScore, which quantifies abrupt fluctuations in multi-turn dialogues. Through both theoretical analysis and empirical validation, we demonstrate that SpikeScore achieves strong cross-domain separability between hallucinated and non-hallucinated responses. Experiments across multiple LLMs and benchmarks demonstrate that the SpikeScore-based detection method outperforms representative baselines in cross-domain generalization and surpasses advanced generalization-oriented methods, verifying the effectiveness of our method in cross-domain hallucination detection.
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