Large Language Models (LLMs) often generate specious hallucinations, creating an urgent need for post-hoc factuality verification against reliable evidence. Existing verification methods incur substantial computational overhead due to joint evidence–claim encoding. While bi-encoders offer a highly efficient alternative, they struggle with asymmetric entailment and are severely vulnerable to contextual noise. To address these challenges, we propose Gated Residual Discrepancy (GRD), a highly efficient bi-encoder framework for factuality verification. To explicitly capture asymmetric entailment, GRD pioneers a difference-dominant paradigm, extracting dual-view vector differences. To mitigate the vulnerability to contextual noise, GRD employs an adaptive gating mechanism that dynamically filters contextual noise, preventing large semantic backgrounds from masking critical errors, thereby enabling highly sensitive verification over broad evidence contexts. Experiments across various benchmarks show GRD achieves 79.99% average Macro-F1, trailing the strongest cross-encoder baseline by only 1.15 points while delivering a 23.55× speedup with only a fraction of the computational FLOPs.

As Large Language Models (LLMs) increasingly generate reasoning-driven outputs that weave isolated events into intricate logical topologies, factuality depends not only on isolated atomic facts but critically on the faithful relations connecting them. However, current verification paradigms prioritize individual facts and remain fundamentally blind to relational distortions. This oversight creates a dangerous false sense of security, where verifiers inadvertently endorse relationally corrupted claims simply because their constituent events are factual. Furthermore, the community lacks a systematic benchmark to evaluate this crucial relational layer. To address these critical vulnerabilities, we introduce BeyondAtoms, a novel benchmark for relational fact verification. Our evaluations reveal that generic verification pipelines often fail by misclassifying relational manipulations as supported. While explicitly guided reasoning models can resolve these structural errors, they incur prohibitive computational costs. To counter this pervasive relation blindness, we propose CARVE, a completely training-free verification framework. By decoupling structural dependencies through deterministic extraction and bi-directional relational alignment, CARVE achieves a favorable accuracy–efficiency trade-off: it remains highly competitive on relational and general fact verification while avoiding the heavy inference cost of reasoning-based LLMs.

Hallucinations arise when large language models (LLMs) guess rather than acknowledge their underlying uncertainty. Existing static strategies for mitigating hallucinations have been only partially successful, largely because they do not explicitly model the information gain from interacting with the external environment. Researchers need a general method to proactively steer users toward informative clarifications, thereby unlocking the model’s effective capacity under underspecified inputs. We model the uncertainty of LLMs in interactive settings and uncover the mechanism of active calibration between model concepts and human evaluations, improving reliability. We show that calibration error in LLMs density estimation admits a non-vanishing lower bound under non-interactive learning, while interaction empirically reduces it. We further characterize that calibration error identifies informative queries and that calibration can be accelerated by shifting query distributions from imbalanced to balanced regimes. Guided by these insights, we propose a calibration-driven Interactive Learning Strategy (ILS) that selects clarification queries by optimizing calibration error, providing both theoretical guarantees and empirical gains for reliability. Code and data are available at https://github.com/zhouyeah215/Demystifying_Uncertainty.

Large language models (LLMs) exhibit remarkable text-generation capabilities, yet struggle with factual consistency, motivating growing interest in factuality verification. Existing factuality verification methods typically follow a Decompose-Then-Verify paradigm, which improves granularity but suffers from poor scalability and efficiency. We propose a novel Decompose-Embed-Interact paradigm that shifts factuality verification from costly text-level reasoning to efficient alignment in embedding space, effectively mitigating the scalability bottlenecks and computational inefficiencies inherent to prior approaches. While the proposed paradigm promises scalable verification, its implementation faces three practical challenges: efficient decomposition, factually faithful embedding, and accurate verification in embedding space. To address these challenges, we introduce E-Verify, a lightweight framework that resolves them through three specially designed modules, each aligned with a specific stage of the paradigm and designed to preserve scalability and efficiency. Experiments demonstrate that E-Verify significantly improves both decomposition and verification efficiency while maintaining competitive accuracy. These results confirm that the proposed paradigm enables scalable and fine-grained factuality verification with minimal performance trade-offs.