Query expansion (QE) is a critical technique in information retrieval that enriches underspecified queries with additional textual context. However, its effect is often unreliable in modern dense retrieval, especially for strong off-the-shelf retrievers without retraining. Existing studies mainly examine expansion quality, semantic drift, or retrieval outcomes, but rarely explain how QE changes dense retrievers internally. In this work, we trace QE effects through sparse autoencoder (SAE) features. Using paired original and expanded queries, we decompose layer-wise retriever representations into sparse latent activations, identify QE-related latents from expansion-induced activation shifts, and interpret them with natural-language descriptions and retrieval cases. Our analysis shows that effective QE induces layer-concentrated changes in sparse latents aligned with retrieval intent and entity attributes, rather than only perturbing final query embeddings. SAE-based activation steering further validates these latents improve retrieval more consistently than random interventions or vanilla QE across four benchmarks, suggesting that SAEs can explain QE effects and offer a lightweight option for precise retrieval behavior modulation without query rewriting or retriever fine-tuning.

Despite the strong reasoning capabilities of recent large language models (LLMs), achieving reliable performance on challenging tasks often requires post-training or computationally expensive sampling strategies, limiting their practical efficiency. In this work, we first show that a small subset of neurons in LLMs exhibits strong predictive correlations with reasoning correctness. Based on this observation, we propose AdaRAS (Adaptive Reasoning Activation Steering), a lightweight test-time framework that improves reasoning reliability by selectively intervening on neuron activations. AdaRAS identifies Reasoning-Critical Neurons (RCNs) via a polarity-aware mean-difference criterion and adaptively steers their activations during inference, enhancing incorrect reasoning traces while avoiding degradation on already-correct cases. Experiments on 10 mathematics and coding benchmarks demonstrate consistent improvements, including over 13% gains on AIME-24 and AIME-25. Moreover, AdaRAS exhibits strong transferability across datasets and scalability to stronger models, outperforming post-training methods without additional training or sampling cost.

Reinforcement learning with verifiable rewards (RLVR) has proven effective in enhancing the reasoning of large language models (LLMs). Monte Carlo Tree Search (MCTS)-based extensions improve upon vanilla RLVR (e.g., GRPO) by providing tree-based reasoning rollouts that enable fine-grained and segment-level credit assignment. However, existing methods still suffer from limited exploration diversity and inefficient reasoning. To address the above challenges, we propose reinforced efficient reasoning via semantically diverse explorations, i.e., ROSE, for LLMs. To encourage more diverse reasoning exploration, our method incorporates a semantic-entropy-based branching strategy and an 𝜀-exploration mechanism. The former operates on already sampled reasoning rollouts to capture semantic uncertainty and select branching points with high semantic divergence to generate new successive reasoning paths, whereas the latter stochastically initiates reasoning rollouts from the root, preventing the search process from becoming overly local. To improve efficiency, we design a length-aware segment-level advantage estimator that rewards concise and correct reasoning while penalizing unnecessarily long reasoning chains. Extensive experiments on various mathematical reasoning benchmarks with Qwen and Llama models validate the effectiveness and efficiency of ROSE. Codes are available at https://github.com/ZiqiZhao1/ROSE-rl.