Multi-turn, long-horizon tasks are increasingly common for large language models (LLMs), but solving them typically requires many sequential model invocations, accumulating substantial inference costs. Here, we study cost-aware multi-turn LLM routing: selecting which model to invoke at each turn from a model pool, given a fixed cost budget. We propose MTRouter, which encodes the interaction history and candidate models into joint history–model embeddings, and learns an outcome estimator from logged trajectories to predict turn-level model utility. Experiments show that MTRouter improves the performance–cost trade-off: on ScienceWorld, it surpasses GPT-5 while reducing total cost by 58.7%; on Humanity’s Last Exam (HLE), it achieves competitive accuracy while reducing total cost by 43.4% relative to GPT-5, and these gains even carry over to held-out tasks. Further analyses reveal several mechanisms underlying its effectiveness: relative to prior multi-turn routers, MTRouter makes fewer model switches, is more tolerant to transient errors, and exhibits emergent specialization across models.Code: https://github.com/ZhangYiqun018/MTRouter

Medical reasoning models remain constrained by parametric knowledge and are thus susceptible to forgetting and hallucinations. DeepResearch (DR) models ground outputs in verifiable evidence from tools and perform strongly in general domains, but their direct transfer to medical field yields relatively limited gains. We attribute this to two gaps: task characteristic and tool-use scaling. Medical questions require evidence interpretation in a knowledge-intensive clinical context; while general DR models can retrieve information, they often lack clinical-context reasoning and thus “find it but fail to use it,” leaving performance limited by medical abilities. Moreover, in medical scenarios, blindly scaling tool-call can inject noisy context, derailing sensitive medical reasoning and prompting repetitive evidence-seeking along incorrect paths. Therefore, we propose DeepMed. For data, we deploy a multi-hop med-search QA synthesis method supporting the model to apply the DR paradigm in medical contexts. For training, we introduce a difficulty-aware turn-penalty to suppress excessive tool-call growth. For inference, we bring a monitor to help validate hypotheses within a controlled number of steps and avoid context rot. Overall, on seven medical benchmarks, DeepMed improves its base model by 9.79% on average and outperforms larger medical reasoning and DR models.

Triple-based Iterative Retrieval-Augmented Generation (iRAG) mitigates document-level noise for multi-hop question answering. However, existing methods still face limitations: (i) greedy single-path expansion, which propagates early errors and fails to capture parallel evidence from different reasoning branches, and (ii) granularity–demand mismatch, where a single evidence representation struggles to balance noise control with contextual sufficiency. In this paper, we propose the Construction–Integration Retrieval and Adaptive Generation model, CIRAG. It introduces an Iterative Construction–Integration module that constructs candidate triples and history-conditionally integrates them to distill core triples and generate the next-hop query. This module mitigates the greedy trap by preserving multiple plausible evidence chains. Besides, to address the granularity–demand mismatch, we propose an Adaptive Cascaded Multi-Granularity Generation module that progressively expands contextual evidence based on the problem requirements, from triples to supporting sentences and full passages. Moreover, we introduce Trajectory Distillation, which distills the teacher model’s integration policy into a lightweight student, enabling efficient and reliable long-horizon reasoning. Extensive experiments demonstrate that CIRAG achieves superior performance compared to existing iRAG methods.