SLMs are increasingly deployed on devices, yet real-world prompts often contain textual or ASR noise that can destabilize model predictions. We analyze this problem from a token-level perspective and find that SLMs exhibit narrow logit margins between the gold token and the top-ranked non-gold token, making noisy prompts more likely to induce local rank flips. To address this issue, we propose LoMaR, a two-stage parameter-efficient framework for robust fine-tuning. In Stage I, LoMaR trains the model on clean prompts with a local logit margin expansion objective to expand the local decision boundary. In Stage II, LoMaR performs residual-subspace adaptation with local logit margin alignment on noisy prompts. After training, the main and residual updates are merged into a standard LoRA adapter, introducing no additional inference cost. Experimental results show that LoMaR outperforms baselines in most noisy settings and achieves lower Performance Drop Rate and Rank Flip Rate. Code and datasets are available at https://github.com/HongJin2828/LoMaR.

Rerankers are critical in Retrieval-Augmented Generation (RAG) for filtering evidence that enhances the accurate generation of LLMs. With the extension to open-domain scenarios, rerankers are inevitably deployed on mixed-style corpora, whereas most existing rerankers are mainly trained on well-edited texts. A rarely explored issue lies in enabling rerankers to maximally capture the effective knowledge for downstream LLMs without being misled by stylistic features. To address this issue, we propose SARK (Style-Adaptive Reranker with Knowledge Prioritization), a style-augmented multi-task framework that prioritizes effective knowledge over stylistic perturbations. SARK performs multi-granular knowledge mining by using an LLM to derive passage-level supervision on whether a passage helps or harms answer correctness, and list-level relative ranking preferences over candidate passages. It then jointly optimizes the reranker model with passage-level classification and list-level ranking objectives via style-augmented multi-task learning, encouraging the model to focus on the information needed for answering under mixed-style scenarios. Extensive experiments demonstrate that SARK improves generation performance across multiple LLMs under mixed-style conditions.