LLM Reliability

LLM-as-Judge systems are widely deployed for automated evaluation, yet practitioners lack reliable methods to know when a judge's verdict should be trusted. Token log-probabilities, the standard post-hoc confidence signal, are unavailable for many commercial LLMs and, even when accessible, saturate above 0.999 with structured JSON output. We introduce VERDI (VERification-Decomposed Inference), a method that extracts confidence from the reasoning trace a structured judge already produces, with no additional inference calls. VERDI decomposes each verification-style evaluation into sub-checks and derives three structural signals: Step-Verdict Alignment, Claim-Level Margin, and Evidence Grounding Score. We combine them with Platt-scaled logistic regression. On three public benchmarks, VERDI achieves AUROC 0.72-0.91 on GPT-4.1-mini and 0.66-0.80 on GPT-5.4-mini. On Qwen3.5-4B/9B/27B, where answer-token logprobs are anti-calibrated (higher confidence on errors, AUROC 0.32-0.49), VERDI achieves 0.56-0.70. We additionally validate on a production system with eight rubrics (AUROC 0.73-0.88 on factual rubrics), demonstrate cross-model transfer (AUROC 0.66-0.69), and show that a 33M-parameter NLI (Natural Language Inference) model provides a scalable alternative to regex extraction.

While existing benchmarks demonstrate the near-perfect performance of large language models (LLMs) on various tasks, this apparent saturation often obscures the need for rigorous evaluation of their reliability. In real-world deployment, however, achieving extremely high reliability (e.g., "five-nines" (99.999%) vs. "three-nines" (99.9%)) is fundamentally critical, as this gap results in an order-of-magnitude increase in failures, which is catastrophic in reliability-critical applications. Still, estimating such a rare failure probability with tight confidence bounds requires prohibitively large LLM inference sizes, making standard Monte Carlo evaluation infeasible under limited compute budgets. In this paper, we observe that LLM failures exhibit strong systematic patterns: across broad parameterized input spaces, a small subset of inputs disproportionately accounts for the majority of failures. Leveraging this observation, we propose to learn a sampling distribution concentrated on failure-prone inputs via the cross-entropy method (CEM). We evaluate our framework on three LLMs, Qwen2.5-Math-7B-Instruct, gpt-oss-20b-low, and Gemini 2.5 Flash Lite, across parameterized GSM8K templates and achieve up to 156.22x reduction in required inferences compared to naive uniform sampling. Our estimates reveal that models with indistinguishable accuracy on standard benchmarks can differ substantially in estimated failure rates, underscoring that reliability is a distinct and measurable axis of model quality. Our simple yet practical framework enables the evaluation of extreme reliability in LLMs, a distinct and underexplored dimension of evaluation beyond existing benchmarks, for their growing use in reliability-sensitive applications.

Guardrail Classifiers defend production language models against harmful behavior, but although results seem promising in testing, they provide no formal guarantees. Providing formal guarantees for such models is hard because "harmful behavior" has no natural specification in a discrete input space: and the standard epsilon-ball properties used in other domains do not carry semantic meaning. We close this gap by shifting verification from the discrete input space to the classifier's pre-activation space, where we define a harmful region as a convex shape enclosing the representations of known harmful prompts. Because the sigmoid classification head is monotonic, certifying the worst-case point is sufficient to certify the entire region, yielding a closed-form soundness proof without approximation in O(d) time. To formally evaluate these classifiers, we propose two constructions of such regions: SVD-aligned hyper-rectangles, which yield exact SAT/UNSAT certificates, and Gaussian Mixture Models, which yield probabilistic certificates over semantically coherent clusters. Applying this framework to three author-trained Guardrail Classifiers on the toxicity domain, every hyper-rectangle configuration returns SAT, exposing verifiable safety holes across all classifiers, despite seemingly high empirical metrics. Probabilistic GMM certificates also expose a divergent structural stability in how these models represent harm. While GPT-2 and Llama-3.1-8B maintain robust coverage of 90% and 80% across varying boundaries, BERT's safety guarantees prove uniquely volatile. This 'coverage collapse' to 55% at the optimal threshold reveals a sparsely populated safety margin in BERT, which only achieves full coverage by adopting an extremely conservative pessimistic threshold. These approaches combined, provide new insights on how effective Guardrail Classifiers really are, beyond traditional red-teaming.

A central challenge in large-scale decision-making under incomplete information is estimating reliable probabilities. Recent approaches use Large Language Models (LLMs) to generate explanatory factors and coarse-grained probability estimates, which are then refined by a Naïve Bayes model over factor combinations. However, sparse factor spaces often yield unknown'' predictions, while expanding factors increases noise and spurious correlations, weakening conditional independence and degrading reliability. To address these limitations, we propose \textsc{Anchor}, an aggregated Bayesian inference framework over a hierarchical factor space. It constructs dense factor hierarchies through iterative generation and clustering, maps contexts via hierarchical retrieval and refinement, and augments Naïve Bayes with a Causal Bayesian Network to model latent factor dependencies. Experiments show that \textsc{Anchor} markedly reduces unknown'' predictions and produces more reliable probability estimates than direct LLM baselines, achieving state-of-the-art performance while significantly reducing time and token overhead.

Retrieval-augmented generation (RAG) improves large language models (LLMs) by incorporating external evidence, but it also introduces knowledge conflicts when retrieved contextual knowledge (CK) and parametric knowledge (PK) disagree or are both unreliable. Existing approaches mainly coordinate which source to use, without explicitly asking whether each answer path is correct. We argue that faithful RAG requires LLM self-awareness, namely the ability to recognize the limits of its own knowledge and reasoning. To ground this problem, we construct a model-specific, ground-truth-aligned knowledge-conflict benchmark by evaluating LLM backbones on PK-only and CK-conditioned answer paths over approximately 69K query-context instances per backbone, drawn from five conflict-QA datasets. We then introduce SABER, a Self-Aware Belief Estimator for RAG that requires no LLM fine-tuning. SABER combines a self-prior with PK-side and CK-side conditional reasoning representations from multi-trace inference, then estimates reliability beliefs with two lightweight predictors to drive a 4-cell decision over trust PK, trust CK, trust either, or abstain. Across four LLM backbones, SABER improves end-to-end accuracy and conflict-specific faithfulness over ten inference-time and fine-tuning baselines, with the largest gains on conflict-heavy datasets. Under abstention, SABER's risk-coverage curve Pareto-dominates every prompt-based abstainer, providing a tunable balance between coverage and answer risk. Our code is available at https://github.com/xizhu1022/SABER.

LLMs can estimate Hospital Anxiety and Depression Scale (HADS) scores from speech in a zero-shot manner, but clinical deployment requires reliability across three dimensions: intra-model consistency, ASR robustness, and evidence faithfulness. We evaluate three LLMs (Phi-4, Gemma-2-9B, and Llama-3.1-8B) on 111 English-speaking participants using ground-truth transcripts and three Whisper ASR variants (Large, Medium, Small), with three independent runs per model-condition pair. We find that (i) Phi-4 and Gemma-2-9B achieve excellent intra-model consistency (ICC > 0.89) with minimal degradation under ASR; (ii) Llama-3.1-8B shows ASR-fragile consistency, with ICC dropping from 0.82 to 0.36 at 10% WER; (iii) predictive validity is largely preserved under ASR for robust models; and (iv) keyword groundedness exceeds 93% for Phi-4 and Gemma-2-9B but falls to 77-81% for Llama-3.1-8B. Inter-model keyword agreement is far lower than score-level agreement, revealing a score-evidence dissociation with implications for clinical interpretability.

Reliable text generation is critical for deploying large language models (LLMs) in real-world applications, particularly in high-stakes domains such as medicine. To improve factual reliability, various inference-time methods have been proposed, including logit-level methods that modify token probability distributions and representation-level methods that manipulate intermediate model representations. However, most existing approaches operate on a single decoding trajectory, limiting their ability to explore alternative reasoning paths and making them susceptible to error accumulation. To address this limitation, we propose Adaptive Path-Contrastive Decoding (APCD), an adaptive multi-path contrastive decoding framework that improves factual reliability without model retraining or fine-tuning. APCD comprises two key components: Entropy-Driven Path Expansion, which adaptively expands the decoding process only at high-uncertainty decision points, and Divergence-Aware Path Contrast, which dynamically regulates contrastive interactions among parallel decoding paths based on their distributional divergence to balance diversity and coherence. We evaluate APCD on four LLM backbones across eight benchmarks spanning both general-domain and medical question answering tasks. Experimental results demonstrate that APCD consistently outperforms strong inference-time baselines in factual accuracy while maintaining competitive inference efficiency. These results demonstrate the robustness and generalizability of APCD across diverse models and tasks, highlighting its effectiveness as a practical multi-path decoding framework for reliable LLM deployment, particularly in high-stakes domains such as medicine. Code is available at https://github.com/zty-king/APCD.

Large language models confidently produce outdated answers, and no existing method can detect them. We show this is not an engineering failure but a structural one: temporal drift, whether a stored fact has changed since training, is encoded as a direction in the residual stream geometrically orthogonal to both correctness and uncertainty. Any method operating on correctness or uncertainty signals is therefore blind to drift by construction. We verify this across six instruction-tuned models. A linear probe trained directly on drift labels achieves AUROC $0.83$--$0.95$; methods based on token entropy, semantic entropy, CCS, and SAPLMA all remain near chance ($0.49$--$0.57$). Five tests confirm the geometric orthogonality: weight cosines ($|\cos| \leq 0.14$), score correlations ($|r| \leq 0.20$), bidirectional null-space projection ($|Δ| \leq 0.008$), iterative null-space projection with $k{=}10$, and difference-of-means dissociation. Mechanistically, the MLP retrieval circuit produces identical dynamics for stale recall and confabulation ($r > 0.81$, six models), explaining why output confidence cannot separate them. A cross-cutoff experiment holds inputs constant and varies only the model: the probe fires on the model whose training predates the fact's transition and stays silent otherwise ($P(A{>}B) = 0.975$--$0.998$, twelve model pairs), confirming it reads model-internal knowledge state rather than input properties. Our code and datasets will be publicly released.

Agents built on large language models (LLMs) rely on a range of reliability techniques, including retry, majority voting, and self-consistency, that have been developed in parallel rather than within a common analytical framework. We observe that an LLM sampled at temperature $T$ is a discrete stochastic channel $p(y \mid x)$ in the sense of Shannon's coding theory, and use this identity as the entry point for such a framework grounded in communication theory. Each of these techniques is a special case of one of six classical reliability operators: diversity combining, hybrid retransmission, iterative generator-critic decoding, rateless sampling, structured redundant verification, and difficulty-adaptive routing. Within the framework we give two closed-form results: a noise-variance threshold above which uniform averaging beats quality-weighted averaging, and a contractivity criterion for generator-critic refinement, consistent with a contractive-to-divergent transition we observe between 3B- and 14B-parameter models. We further introduce a cost-aware semantic-nearest-neighbor router whose single Lagrangian knob traverses the quality-cost frontier without retraining. Across six channel configurations spanning local and cloud models on 69 hard tasks, no fixed model-technique-budget choice dominates, motivating per-task allocation. On a 300-item hard split of MMLU, GSM8K, and HumanEval, our router occupies the full empirical Pareto frontier: at matched quality, its normalized cost is ${\approx}56$% lower than the strongest fixed technique; at matched normalized cost, it improves quality by ${\approx}7$% ($26$% over single-shot decoding). These results argue for consolidating these reliability techniques into a single tunable layer informed by channel coding.

Evaluating whether Multimodal Large Language Models can produce trustworthy, verifiable reasoning over long, visually rich documents requires evaluation beyond end-to-end answer accuracy. We introduce DocScope, a benchmark that formulates long-document QA as a structured reasoning trajectory prediction problem: given a complete PDF document and a question, the model outputs evidence pages, supporting evidence regions, relevant factual statements, and a final answer. We design a four-stage evaluation protocol -- Page Localization, Region Grounding, Fact Extraction, and Answer Verification -- that audits each level of the trajectory independently through inter-stage decoupling, with all judges selected and calibrated via human alignment studies. DocScope comprises 1,124 questions derived from 273 documents, with all hierarchical evidence annotations completed by human annotators. We benchmark 6 proprietary models, 12 open-weight models, and several domain-specific systems. Our experiments reveal that answer accuracy cannot substitute for trajectory-level evaluation: even among correct answers, the highest observed rate of complete evidence chains is only 29%. Across all models, region grounding remains the weakest trajectory stage. Furthermore, the primary difficulty stems from aggregating evidence dispersed across long distances and multiple document clusters, while an oracle study identifies faithful perception and fact extraction as the dominant capability bottleneck. Cross-architecture comparisons further suggest that activated parameter count matters more than total scale. The benchmark and code will be publicly released at https://github.com/MiliLab/DocScope.

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem$_1$-ECE, the same-sample self-consistency score, and Sem$_2$-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem$_2$ achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

Hallucination detection methods for large language models increasingly operate on chain-of-thought reasoning traces, yet it remains unclear whether they evaluate the reasoning itself or merely exploit surface correlates of the final answer. We introduce a controlled-invariance methodology that exposes this distinction through two oracle tests: \textsc{Force}, which replaces each response's final answer with the ground truth while preserving the reasoning trace, and \textsc{Remove}, which strips answer-announcement steps while leaving the trajectory intact. This reveals if their predictive power derives from answer-level artifacts rather than from the structure or validity of intermediate reasoning. We further show that once these artifacts are controlled for, effective detection does not necessarily require complex learned representations: TRACT, a lightweight scorer built on lexical trajectory features (hedging trends, step-length dynamics, and cross-response vocabulary convergence), achieves strong robustness while remaining competitive with or outperforming existing baselines on unperturbed traces. These findings suggest that the current central challenge in reasoning-aware hallucination detection is not the absence of signal in the trace, but the failure to isolate it from endpoint cues.

Large Language Models (LLMs) are increasingly used in settings where reliable self-assessment is critical. Assessing model reliability has evolved from using probabilistic correctness estimates to, more recently, eliciting verbalized confidence. Confidence, however, has been shown to be an inconsistent and overoptimistic predictor of model correctness. Drawing on cognitive appraisal theory, a framework from human psychology that decomposes self-evaluation into multiple components, we propose a multidimensional perspective on model self-assessment. We elicit six appraisal-based dimensions of self-assessment, alongside confidence, and evaluate their utility for predicting model failure across 12 LLMs and 38 tasks spanning eight domains. We find that competence-related appraisal dimensions, particularly effort and ability, consistently match or outperform confidence across most settings. Effort additionally yields less overoptimistic estimates that remain stable across model sizes. In contrast, affective dimensions provide marginally predictive signals. Furthermore, the most informative dimension varies systematically with task characteristics: effort is most predictive for reasoning-intensive tasks, while ability and confidence dominate on retrieval-oriented tasks. Broadly, our findings indicate that structured multidimensional self-assessment is a promising approach to improving the reliability and safety of language model deployment across diverse real-world settings.

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, prefix consistency, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by it reaches Standard MV plateau accuracy at up to 21x fewer tokens (median 4.6x). Our code is available at https://github.com/naoto-iwase/prefix-consistency.

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.

We introduce a proxy-analyzer framework for detecting hallucinations in large language models. Instead of looking inside the generating model, our system reads already-generated text through a small locally hosted open-weight model and spots hallucinations using the reader's own internal activations. This works just as well when the generator is a closed API like GPT-4 as when it is any open-weight model. We built eighteen features grounded in how transformers process text, covering residual stream norms, per-head source-document attention, entropy, MLP activations, logit-lens trajectories, and three new token-level grounding statistics. We trained a stacking ensemble on 72,135 samples from five hallucination datasets. We tested across seven analyzer architectures from 0.5 billion to 9 billion parameters: Qwen2.5 at 0.5B and 7B, Gemma-2 at 2B and 9B, Pythia at 1.4B, and LLaMA-3 at both 3B and 8B. Across all seven, we consistently beat ReDeEP's token-level AUC of 0.73 on RAGTruth by 7.4 to 10.3 percentage points. Qwen2.5-7B reached an F1 of 0.717, just above ReDeEP's 0.713, while Qwen2.5-0.5B hit 0.706. The most striking finding is how tightly all seven models cluster: AUC spans only 2.3 percentage points across an eighteen-fold difference in model size. Even more surprising, our 3B LLaMA outperforms our 8B LLaMA on RAGTruth, showing that bigger is not always better even within the same model family. Both RAGTruth and LLM-AggreFact include outputs from multiple LLM families, so our results are not skewed toward any particular generator.

Existing Large Language Model (LLM) benchmarks primarily focus on syntactically correct inputs, leaving a significant gap in evaluation on imperfect text. In this work, we study how word-boundary corruption affects how LLMs detect targeted information. By inserting whitespace characters within words to break them into fragments, LLMs' detection accuracy follows a U-shaped curve with the increase in insertion rate. We refer to this curve as the Text Uncanny Valley. To explain such observation, we propose a mode transition hypothesis: LLMs operate in a word-level mode for near-normal text and a character-level mode for heavily fragmented text, with the valley marking the disordered transition where neither mode is effective. Four experiments and one analysis are consistent with this account: in-context learning fails to rescue valley-bottom performance; regularizing the perturbation substantially reduces the U-shape; a math reasoning task replicates the U-shape for Gemini 3.0 Flash but not for stronger models, suggesting the effect is attenuated when tasks rely less on exact lexical alignment; and tokenization entropy peaks before the F1 minimum, consistent with a regime-conflict interpretation. These findings reveal a failure mode invisible to clean-text benchmarks yet directly relevant to any deployment scenario involving noisy or uncurated text inputs.

Large Language Models for code generation frequently produce hallucinations in Fill-in-the-Middle (FIM) tasks -- plausible but incorrect completions such as invented API methods, invalid parameters, undefined variables, or non-existent imports. These failures pass superficial review yet introduce runtime errors. We introduce Delulu, a verified multi-lingual benchmark of 1,951 FIM samples across 7 languages and 4 hallucination types. Samples are curated through an adversarial pipeline: a frontier LLM generates plausible hallucinations, four diverse judge models evaluate them, embedding-based clustering mines progressively harder examples, self-contained Docker containers verify that golden completions compile while hallucinated variants produce the expected runtime error, and a final human-expert review removes any remaining biased or trivially decidable samples. We evaluate 11 open-weight FIM models from five families spanning 0.5B-32B parameters: a six-point Qwen2.5-Coder scaling slate, plus a cross-family slate (CodeLlama, DeepSeek-Coder-V2, StarCoder2). The strongest model reaches only 84.5% pass@1, no family exceeds 0.77 Edit Similarity, and every family produces hallucination-aligned completions on a non-trivial share of samples, confirming that the difficulty exposed by Delulu is task-intrinsic rather than family-specific. We release the benchmark, containers, and evaluation framework at https://github.com/microsoft/delulu.

Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge whether an output should be trusted. Existing methods require one or more full autoregressive generations to estimate uncertainty, which introduces substantial inference cost and often delays uncertainty assessment. In this paper, we investigate whether effective uncertainty estimation can be achieved with partial generation or even input-only information. Specifically, we first develop a unified framework that formulates uncertainty estimation as an early estimation problem over the autoregressive generation process of LLMs. This framework organises existing and proposed estimators by the information they observe, ranging from multi-generation to input-only prediction, and clarifies the performance-cost trade-off underlying different uncertainty estimation methods. Building on this view, we study two largely underexplored low-cost settings: estimating uncertainty with part of the generation, and predicting uncertainty from the input prompt. We propose Logit Magnitude, which uses top-M logit evidence to estimate uncertainty from an early-stopped generation prefix, and MetaUE, which distils generation-based uncertainty into a lightweight input-only estimator trained with uncertainty scores. Extensive experiments on general and domain-specific benchmarks show that Logit Magnitude achieves strong performance, and partial generations of LLMs are often sufficient for effective uncertainty estimation. MetaUE further provides a competitive input-only approximation in several settings. These findings suggest that effective uncertainty estimation requires less generation than commonly assumed, enabling unreliable responses to be identified earlier.

LLMs reliably correct false claims when presented in isolation, yet when the same claims are embedded in task-oriented requests, they often comply rather than correct. We term this failure mode \emph{correction suppression} and construct a benchmark of 300 false premises to systematically evaluate it across eight models. Suppression rates range from 19% to 90%, with four models exceeding 80%, establishing correction suppression as a prevalent and severe phenomenon. Mechanistic analysis reveals that suppression is not a knowledge failure: the model registers the error internally but task context diverts early-layer attention from the false claim as output intent crystallizes toward compliance at middle layers. We characterize this as \emph{knowing but not correcting} -- suppression occurs at response selection rather than knowledge encoding. Guided by this mechanism, we propose two training-free interventions. Correction Direction Steering (CDS) estimates a correction-compliance direction from matched pairs and injects it at middle layers before output intent crystallizes. Dynamic Payload Amplification (DPA) localizes payload tokens via attention divergence between early and late layers and amplifies their representation at the final layer, requiring no calibration data. Experiments on Qwen3.5-9B and LLaMA3.1-8B show both methods substantially improve factual strictness. CDS achieves the highest correction rate on Qwen3.5-9B (0%$\to$58.2%). DPA is the only method that preserves or improves reasoning capability on both models. These findings introduce \emph{factual strictness} -- the willingness to uphold accuracy against contextual pressures -- as a new dimension of model reliability.

One of the most critical challenges in Large Language Models is their tendency to hallucinate, i.e., produce factually incorrect responses. Existing approaches show promising results in terms of hallucination correction, but still suffer from a main limitation: they apply corrections indiscriminately to every token, corrupting also the originally correct generations. To overcome this drawback, we propose PCNET, a Probabilistic Circuit trained as a tractable density estimator over the LLM residual stream. The method detects hallucinations as geometric anomalies on the factual manifold, which is done via exact Negative Log-Likelihood computation, hence without the need for sampling, external verifiers, or weight modifications, as in existing techniques. To demonstrate its effectiveness, we exploit PCNET as a dynamic gate that distinguishes hallucinated from factual hidden states at each decoding step. This triggers our second main contribution, PC-LDCD (Probabilistic Circuit Latent Density Contrastive Decoding), only when the latent geometry deviates from factual regions, while leaving correct generations untouched. Across four LLMs, ranging from 1B to 8B models, and four benchmarks covering conversational reasoning, knowledge-intensive QA, reading comprehension, and truthfulness, PCNET achieves near-perfect hallucination detection across CoQA, SQuAD v2.0, and TriviaQA, with AUROC reaching up to 99%. Moreover, PC-LDCD obtains the highest True+Info, MC2, and MC3 scores on TruthfulQA in three out of four models, in comparison with state-of-the-art baselines, while reducing the mean corruption rate to 53.7% and achieving a preservation rate of 79.3%. Our proposed method is publicly available on GitHub.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a \emph{harness} system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76% of cases. Our ReFlect harness achieves task success rates ranging from 41% on gpt-4o-mini to 56% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0% (Direct CoT) to between 82% (Qwen2.5-72B) and 87% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

We propose a lightweight and single-pass uncertainty quantification method for detecting hallucinations in Large Language Models. The method uses attention matrices to estimate uncertainty without requiring repeated sampling or external models. Specifically, we measure the Kullback-Leibler divergence between each attention head's distribution and a uniform reference distribution, and use these features in a logistic regression probe. Across multiple datasets, task types, and model families, attention divergence is highly predictive of answer correctness and performs competitively with existing uncertainty estimation methods. We find that this signal is concentrated in middle layers and on factual tokens such as named entities and numbers, suggesting that attention dynamics provides an efficient and interpretable white-box signal of model uncertainty.

This paper presents NoisyCoconut, a novel inference-time method that enhances large language model (LLM) reliability by manipulating internal representations. Unlike fine-tuning methods that require extensive retraining, NoisyCoconut operates directly on model representations during inference and requires no retraining. Rather than training models to reason in latent space, we inject controlled noise into latent trajectories to generate diverse reasoning paths. Agreement among these paths provides a confidence signal, enabling models to abstain when uncertain. We demonstrate that this approach achieves effective coverage-accuracy tradeoffs across multiple reasoning benchmarks without requiring access to training data or modification of model parameters. This approach provides a practical pathway to improving the reliability of LLM outputs while maintaining compatibility with existing models. Our experiments show that unanimous agreement among noise-perturbed paths reduces error rates from 40-70% to below 15%, enabling models to exceed 95% accuracy on mathematical reasoning tasks through selective abstention.

When the substantive content of a request is rewritten, do large language models still answer in the format the original task asked for? We find that they often do not, even at temperature zero. On a 150-query evaluation over five compact 2025-era LLMs and four task types, we observe a systematic failure mode we call prompt-variant output-mode collapse: when a closed-form prompt asks for a bare label or a single choice token, content-preserving prompt variants can push the model into conversational prose, the requested format dissolves, and exact-match evaluation pipelines silently misjudge the result. To make this measurable, we release PARACONSIST, a 900-prompt benchmark of 150 base queries with five lexical, syntactic, and semantic-expansion prompt variants each, and a Semantic Consistency Score that decomposes prompt-variant robustness into answer consistency, sentence-BERT semantic similarity, and length stability. Under a whole-word answer-set match, only ~22% of closed-form variant responses preserve the ground-truth label inside their output, while ~78% drift away from the answer space entirely. In our pool, the dominant predictor of collapse is task structure rather than model identity, with model differentiation jointly carried by answer consistency and length stability. Robustness audits should therefore track response-mode preservation as a first-class reliability target alongside answer accuracy.

Multi-constraint instruction following requires verifying whether a response satisfies multiple individual requirements, yet LLM judges are often assessed only through overall-response judgments. We introduce MCJudgeBench, a benchmark for constraint-level judge evaluation in multi-constraint instruction following. Each instance includes an instruction, a candidate response, an explicit constraint list, per-constraint gold labels in {yes, partial, no}, and controlled response-side perturbations. The evaluation protocol further includes evaluation prompt variants to test judge stability. We evaluate proprietary and open-source LLM judges using both correctness and inconsistency metrics, distinguishing intrinsic inconsistency under stochastic decoding from procedural inconsistency under prompt and response perturbations. Our results show that judge reliability has multiple dimensions: strong overall performance does not guarantee equally reliable detection across label categories, especially for rarer partial and no cases. Judges with higher correctness do not always have lower inconsistency. Evaluation with reasoning improves correctness but does not uniformly improve stability. These findings motivate evaluating LLM judges at the constraint level to study these failure modes.

Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM inference under conditional-i.i.d. calls. One labeled call identifies the mean latent success probability; two labeled calls identify its second moment and hence the same-example correctness correlation that separates stable errors from recoverable call-level randomness. From these two moments, every fixed majority-vote budget has a sharp distribution-free two-call interval. The key technical reduction is that the infinite-dimensional moment problem has three-atom extremizers and quadratic dual certificates for every finite budget, so the bounds are exact rather than discretized or parametric. The first useful budget, three votes, has a closed form, width at most $1/8$, and a certified-improvement criterion. The infinite-vote endpoint is the limit of majority voting as the number of calls tends to infinity; it is also sharply bounded, but remains threshold-sensitive because it depends on latent mass around $q=1/2$. We add maximum-entropy and Latent-difficulty Gaussian-probit point completions, and experiments on LLM calls over QNLI and QQP show that empirical three- and five-vote accuracies are contained in the projected two-call regions while temperature changes and randomized model mixtures can create voting gains not ordered by one-call accuracy.

A reliable language model should be able to signal, prior to generation, when a query falls outside its knowledge. We investigate whether representation geometry can provide such a pre-generation signal by measuring the deviation of hidden states from an answerable reference set, requiring no labeled failure data and no access to model outputs. Across three instruction-tuned models (Llama 3.1-8B, Qwen 2.5-7B, and Mistral-7B-Instruct) and three prompt forms (Math, Fact, Code), we find that geometry primarily encodes task form. Within mathematical prompts, unanswerable inputs consistently deviate from the answerable centroid, yielding strong separation (ROC-AUC 0.78-0.84). This single-pass pre-generation signal outperforms a simple refusal baseline and compares favorably to self-consistency. It also captures cases where models do not explicitly refuse. In contrast, no reliable geometric signal emerges for factual prompts, indicating that the effect is form-conditional rather than universal. Code prompts show large effect sizes with higher variance, suggesting partial generalization beyond mathematical form. A layer-wise analysis reveals that the signal arises in early layers and gradually attenuates toward the output. These results suggest that answerability-related geometry is established before the final stages of generation. Together, these findings indicate that geometric deviation can serve as a lightweight pre-generation signal that is reliable in structured domains with formal answerability constraints, with clear boundaries on where it generalizes.

Most hallucination evaluations focus on English, leaving it unclear whether findings transfer to lower-resource languages. We investigate faithfulness hallucinations, defined as model-generated content that is fluent and plausible but diverges from the provided input or is internally inconsistent. Leveraging the multilingual MultiWikiQA dataset, we utilize the LettuceDetect framework to create synthetic hallucination datasets for 306 languages, from which we train token-level hallucination classifiers for 30 European languages. In this work, we present evaluations of model hallucinations on a selection of languages: English, Danish, German, and Icelandic. Using these classifiers, we evaluate the hallucination rates for Qwen3-0.6B, Qwen3-14B, Gemma-3-12B-IT, cogito-v1-preview-qwen-32B, and cogito-v1-preview-llama-70B. Our classifiers reveal notably higher hallucination rates for Qwen3-0.6B (up to 60% of answers containing at least one hallucination, peaking in Icelandic) and generally lower rates for larger models, with cogito-v1-preview-qwen-32B and cogito-v1-preview-llama-70B performing best on most languages. Hallucination rates are consistently higher for lower-resource languages, particularly Icelandic.