Large language models (LLMs) are increasingly used as evaluators to assess output quality and preference alignment, yet providing reliable guarantees of agreement with human judgments remains challenging. Recent work introduces confidence-thresholding methods that provide such guarantees for pairwise comparisons, relying on the assumption that higher estimated confidence implies lower disagreement risk with humans. However, this assumption can break down when the number of candidate responses increases, since distributing probability mass across many alternatives can distort confidence estimates. To address this issue, we propose a Localize-Then-Decide framework. First, conformal prediction localizes a small shortlist that contains the human-preferred response with high probability. Then, a calibrated confidence-based rule selectively chooses a single response from this shortlist or abstains. This design restores the monotonic relationship between confidence and disagreement risk and enables high-probability agreement guarantees. Experiments with multiple candidate sizes across several datasets and judge LLMs demonstrate that our framework consistently achieves higher guarantee success rates and substantially higher coverage than single-stage baselines.

Radiology report generation involves translating visual signals from pixels into precise clinical language. Existing encoder-decoder models often suffer from hallucinations, generating plausible but incorrect medical findings. We propose GraphRAG-Rad, a novel architecture that integrates biomedical knowledge through a novel Latent Visual-Semantic Retrieval (VSR). Unlike traditional Retrieval-Augmented Generation (RAG) methods that rely on textual queries, our approach aligns visual embeddings with the latent space of the Knowledge Graph, PrimeKG. The retrieved sub-graph guides the Visual Encoder and the Multi-Hop Reasoning Module. The reasoning module simulates clinical deduction paths (Ground-Glass Opacity → Viral Pneumonia → COVID-19) before it combines the information with visual features in a Graph-Gated Cross-Modal Decoder. Experiments on the COV-CTR dataset demonstrate that GraphRAG-Rad achieves competitive performance with strong results across multiple metrics. Furthermore, ablation studies show that integrating latent retrieval and reasoning improves performance significantly compared to a visual-only baseline. Qualitative analysis further reveals interpretable attention maps. These maps explicitly link visual regions to symbolic medical concepts, effectively bridging the modality gap between vision and language.