Entropy mechanism emerges as a key organizing principle for understanding and improving Large Reasoning Models (LRMs). This survey examines how entropy shapes both their training and inference behavior. On the training side, we take a mathematical perspective: casting existing RL-based reasoning algorithms into a unified objective and using this formulation to derive an entropy-centric decomposition of methods, clarifying how different approaches adjust exploration–exploitation "knobs". On the inference side, based on the characteristic of LRM that trading increased inference tokens yields better performance, we summarize methods that leverage entropy to enhance inference performance or reduce uncertainty. Finally, we discuss open challenges and future directions of entropy-driven research for LRMs. Our repository is available on https://anonymous.4open.science/r/Awesome_LRM_with_Entropy-0503.

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.

Recent LLM-based recommenders enhance language models with collaborative embeddings from user-item interactions, but making such embeddings available does not ensure their proper use during inference. Through a diagnostic attention analysis, we find that the utilization of collaborative embeddings is depth-dependent and alignment-sensitive, suggesting that LLMs need to balance their internal semantic knowledge with external collaborative knowledge. To address this issue, we propose SAILRec, an LLM-based recommender that improves this balance through dual-side semantic alignment and hierarchical attention steering. The former aligns item-side embeddings with item-text semantics and user-side embeddings with codebook-based semantic profiles, while the latter suppresses premature shallow-layer collaborative interference and strengthens collaborative evidence in deeper decision layers. Experiments on MovieLens-1M and Amazon-Book show that SAILRec consistently outperforms representative baselines, with ablation and masking analyses validating its key designs. Our implementation is available at https://github.com/XuPhoenixyear/SAILRec.

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

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.

Current conversational recommendation systems focus predominantly on text. However, real-world recommendation settings are generally multimodal, causing a significant gap between existing research and practical applications. To address this issue, we propose Muse, the first multimodal conversational recommendation dataset. Muse comprises 83,148 utterances from 7,000 conversations centered around the Clothing domain. Each conversation contains comprehensive multimodal interactions, rich elements, and natural dialogues. Data in Muse are automatically synthesized by a multi-agent framework powered by multimodal large language models (MLLMs). It innovatively derives user profiles from real-world scenarios rather than depending on manual design and history data for better scalability, and then it fulfills conversation simulation and optimization. Both human and LLM evaluations demonstrate the high quality of conversations in Muse. Additionally, fine-tuning experiments on three MLLMs demonstrate Muse’s learnable patterns for recommendations and responses, confirming its value for multimodal conversational recommendation. Our dataset and codes are available at https://anonymous.4open.science/r/Muse-0086.