When to Retrieve During Reasoning: Adaptive Retrieval for Large Reasoning Models

Although precise recall is a core objective in Retrieval-Augmented Generation (RAG), a critical oversight persists in the field: improvements in retrieval performance do not consistently translate to commensurate gains in downstream reasoning. To diagnose this gap, we propose the Recall Conversion Rate (RCR), a novel evaluation metric to quantify the contribution of retrieval to reasoning accuracy. Our quantitative analysis of mainstream RAG methods reveals that as Recall@5 improves, the RCR exhibits a near-linear decay. We identify the neglect of retrieval quality in these methods as the underlying cause. In contrast, approaches that focus solely on quality optimization often suffer from inferior recall performance. Both categories lack a comprehensive understanding of retrieval quality optimization, resulting in a trade-off dilemma. To address these challenges, we propose comprehensive retrieval quality optimization criteria and introduce the NeocorRAG framework. This framework achieves holistic retrieval quality optimization by systematically mining and utilizing Evidence Chains. Specifically, NeocorRAG first employs an innovative activated search algorithm to obtain a refined candidate space. Then it ensures precise evidence chain generation through constrained decoding. Finally, the retrieved set of evidence chains guides the retrieval optimization process. Evaluated on benchmarks including HotpotQA, 2WikiMultiHopQA, MuSiQue, and NQ, NeocorRAG achieves SOTA performance on both 3B and 70B parameter models, while consuming less than 20% of tokens used by comparable methods. This study presents an efficient, training-free paradigm for RAG enhancement that effectively optimizes retrieval quality while maintaining high recall. Our code is released at https://github.com/BUPT-Reasoning-Lab/NeocorRAG.

Retrieval-augmented generation (RAG) has proven effective for knowledge-intensive tasks, but is widely believed to offer limited benefit for reasoning-intensive problems such as math and code generation. We challenge this assumption by showing that the limitation lies not in RAG itself, but in the choice of corpus. Instead of retrieving documents, we propose retrieving thinking traces, i.e., intermediate thinking trajectories generated during problem solving attempts. We show that thinking traces are already a strong retrieval source, and further introduce T3, an offline method that transforms them into structured, retrieval-friendly representations, to improve usability. Using these traces as a corpus, a simple retrieve-then-generate pipeline consistently improves reasoning performance across strong models and benchmarks such as AIME 2025--2026, LiveCodeBench, and GPQA-Diamond, outperforming both non-RAG baselines and retrieval over standard web corpora. For instance, on AIME 2025-2026, RAG with traces generated by Gemini-2-thinking achieves relative gains of +56.3%, +8.6%, and +7.6% for Gemini-2.5-Flash, GPT-OSS-120B, and GPT-5, respectively, even though these are more recent models. Overall, our results suggest that thinking traces are an effective retrieval corpus for reasoning tasks, and transforming them into structured, compact, or diagnostic representations unlocks even stronger gains. Code available at https://github.com/Narabzad/t3.

Retrieval-augmented generation (RAG) has become a standard mechanism for grounding language models in external knowledge, yet conventional retrieval based on lexical or semantic similarity is poorly suited for complex reasoning tasks: a semantically similar problem may demand an entirely different solution strategy, while a superficially different problem may share the same underlying reasoning pattern. We propose Retrieval-Augmented Reinforcement Fine-Tuning (RA-RFT), a post-training framework that teaches language models to reason by analogy. RA-RFT uses gold-relevance distillation to train a retriever that ranks contexts by expected reasoning benefit rather than semantic overlap, and then fine-tunes the policy model via reinforcement fine-tuning methods with retrieved analogous demonstrations, so the model learns to leverage reasoning traces under verifiable outcome rewards. We further analyze the diversity of retrieved contexts and find that reasoning-aware retrieval surfaces complementary solution strategies that provide distinct reasoning scaffolds for individual problems. Across challenging mathematical reasoning benchmarks, RA-RFT consistently outperforms standard reinforcement fine-tuning methods. For example, it improves AIME 2025 average@32 accuracy by 7.1 and 2.8 points over GRPO for Qwen3-1.7B and Qwen3-4B respectively -- suggesting that reasoning-aware retrieval is a complementary axis of improvement and orthogonal to advances in reward design or training curricula.