Large language models increasingly express uncertainty through verbalized confidence, yet these expressions often fail to reflect the model’s sampled behavior. We study verbal confidence alignment as a distributional calibration problem, where the confidence target for a prompt is estimated from repeated model outputs rather than from a single response. However, group rollouts alone are insufficient, since the resulting target must provide a useful training signal. We propose Semantic-Answer Guided Entropy (SAGE), 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 introduce Group-Uncertainty Preference Optimization (GUPO), an uncertainty-channel training framework that supervises verbal confidence expressions rather than the full response. Experiments across factual, mathematical, and multiple-choice reasoning tasks show improved confidence ranking, lower calibration error, and reduced overconfidence.

Diet plays a central role in human health, and Nutrition Question Answering (QA) offers a promising path toward personalized dietary guidance and the prevention of diet-related chronic diseases. However, existing methods face two fundamental challenges: the limited reasoning capacity of single-agent systems and the complexity of designing effective multi-agent architectures, as well as contextual overload that hinders accurate decision-making. We introduce Nutritional-Graph Router (NG-Router), a novel framework that formulates nutritional QA as a supervised, knowledge-graph–guided multi-agent collaboration problem. NG-Router integrates agent nodes into heterogeneous knowledge graphs and employs a graph neural network to learn task-aware routing distributions over agents, leveraging soft supervision derived from empirical agent performance. To further address contextual overload, we propose a gradient-based subgraph retrieval mechanism that identifies salient evidence during training, thereby enhancing multi-hop and relational reasoning. Extensive experiments across multiple benchmarks and backbone models demonstrate that NG-Router consistently outperforms both single-agent and ensemble baselines, offering a principled approach to domain-aware multi-agent reasoning for complex nutritional health tasks.

Large language models (LLMs) and agent-based frameworks have advanced rapidly, enabling diverse applications. Yet, with the proliferation of models and agentic strategies, practitioners face substantial uncertainty in selecting the best configuration for a downstream task. Prior studies show that different agents and backbones exhibit complementary strengths, and that larger models are not always superior, underscoring the need for adaptive routing mechanisms. Existing approaches to agent routing, however, often emphasize cost efficiency while overlooking the fine-grained contextual and relational structure inherent in QA tasks. In this paper, we propose AgentRouter, a framework that formulates multi-agent QA as a knowledge-graph–guided routing problem supervised by empirical performance signals. Specifically, we convert QA instance into a heterogeneous knowledge graph that jointly encodes queries, contextual entities, and agents, and then train a heterogeneous graph neural network (GNN) to propagate information across node types and produce task-aware routing distributions over agents. By leveraging soft supervision and weighted aggregation of agent outputs, AgentRouter learns principled collaboration schemes that capture the complementary strengths of diverse agents. Extensive experiments demonstrate that our framework consistently outperforms single-agent and ensemble baselines, while generalizing across benchmarks and LLM backbones. These results highlight the effectiveness and robustness of graph-supervised multi-agent routing for question answering. Our code repo is available at https://anonymous.4open.science/r/AgentRouter.