Judge, Retrieve, or Abstain: Uncertainty-Guarded LLM Judging with Provable Risk Guarantees

Using LLMs as judges has become standard practice for evaluating model outputs at scale. This is particularly common for subjective, open-ended tasks such as assessing helpfulness or alignment, where no single reference answer exists. However, objective tasks introduce a distinct reliability challenge for reference-free LLM judging. In the absence of a reference answer, the judge evaluates factual correctness either through its parametric knowledge or through tool augmentation. Although the former enables efficient evaluation, the judge may hallucinate or lack sufficient evidence for its verdict. Conversely, tool augmentation can provide additional evidence but introduces extra computational cost and requires an appropriate mechanism to determine when and how that evidence should be used reliably. More importantly, neither approach alone provides formal control over the risk of accepted verdicts or guarantees their reliability at a specified level. We propose a risk-controlled framework that calibrates uncertainty thresholds on a held-out set so that the false discovery rate among accepted verdicts remains below a user-specified level~$α$ with high probability, using finite-sample Clopper--Pearson intervals. When the parametric mode is not sufficiently confident, the instance is routed to a retrieval-augmented mode, where the judge gathers web evidence and re-evaluates the instance under a second calibrated threshold. The finite-sample guarantee carries over to this two-threshold routing without additional assumptions. Across open-domain QA benchmarks and judges of varying scales, the framework maintains the target error rate while achieving substantially higher coverage than single-mode baselines.

Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs

Metacognition is a critical component of intelligence that describes the ability to monitor and regulate one's own cognitive processes. Yet LLMs exhibit systemic deficiencies in key metacognitive faculties: they hallucinate with high confidence, fail to recognize knowledge boundaries, and misrepresent their internal uncertainty--undermining trustworthiness and reliability. Since monitoring task performance and adapting behavior accordingly are central to metacognition, we posit that models capable of accurately judging their own performance are better positioned to improve it. We operationalize this idea via two novel mechanisms: reinforcement learning with metacognitive feedback (RLMF), a paradigm to refine completion rankings during preference optimization based on the quality of a model's self-judgments of performance, and metacognitive data selection, which uses similar self-judgments to identify high-value training examples, outperforming naive active learning. We apply these innovations to the problem of faithful calibration (FC), a task that is itself fundamentally metacognitive: the goal is to align expressed with intrinsic uncertainty, difficult even for frontier LLMs. We adopt a two-stage, decoupled approach, first using these methods to calibrate the faithfulness of models' self-reported confidence scores, then mapping to natural, context-adaptable linguistic uncertainty via targeted output editing. Extensive experiments show RLMF achieves generalizable, state-of-the-art FC on diverse tasks while preserving accuracy. Further, RLMF surpasses standard RL by up to 63% while enhancing models' ability to assess and express their own capability limits. This positions RLMF as a promising paradigm to enhance LLM metacognition toward improved abilities and alignment, and suggests metacognitive performance as an effective RL signal to overcome limits of prior intrinsic feedback methods.

BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning

While Low-rank adaptation (LoRA) enables highly efficient fine-tuning by constraining task-specific updates to fixed low-rank subspaces, this rigid design limits representational flexibility and often results in overconfident predictions and miscalibrated uncertainty, especially in low-data regimes. Recent Bayesian LoRA variants improve uncertainty estimation by modeling posterior distributions over adaptation parameters. However, these approaches typically rely on fixed or heuristically determined ranks, overlooking the inherently context-dependent nature of adaptation capacity. In this paper, we propose BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning. Drawing inspiration from probabilistic topic models, BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. This Bayesian formulation provides principled, data-driven capacity control, mitigating over-parameterization while preserving expressiveness. Beyond the modeling contribution, we provide a complexity-theoretic generalization analysis showing that the generalization gap of BaRA depends on the learned joint effective rank $\bar{s}_{Φ,θ}$ induced by the global-local gate, rather than the maximum rank $r$. This result explains why sparse adaptive rank allocation can reduce the effective hypothesis complexity while preserving input-dependent expressiveness. Extensive experiments on diverse natural language benchmarks demonstrate that BaRA consistently improves predictive performance, robustness, and uncertainty calibration compared to standard LoRA and existing Bayesian LoRA variants.

SAGE: Answer-Conditioned Uncertainty Targets for Verbal Uncertainty Alignment

Large language models increasingly express uncertainty through natural-language statements, yet these expressions often fail to reflect the model's sampled behavior. We study verbal uncertainty alignment as a distributional calibration problem: the appropriate uncertainty target for a prompt should be estimated from repeated model outputs rather than from an isolated response. However, group rollouts alone are insufficient, since the resulting target must provide a useful training signal. Existing targets only partially satisfy this requirement. We propose SAGE, Semantic-Answer Guided Entropy, a group-level uncertainty target that constructs an answer-conditioned uncertainty geometry over sampled responses. SAGE preserves categorical, numeric, and symbolic answer distinctions while maintaining a smooth and scale-preserving calibration signal. We further apply this target through Group-Uncertainty Preference Optimization, or GUPO, an uncertainty-channel training framework that supervises verbal uncertainty expressions rather than the full response. Experiments across factual, mathematical, and multiple-choice reasoning tasks show improved uncertainty ranking, lower calibration error, and reduced overconfidence.