Group Relative Policy Optimization (GRPO) improves LLM reasoning, but LoRA-based GRPO can underperform when the initialized adapter subspace is poorly aligned with reward-induced gradients. We propose GRAIL, Gradient-Reward Aligned Initialization for LoRA-based GRPO, which estimates reward-aligned gradients from grouped rollouts before policy optimization and uses them to construct LoRA factors. The full GRAIL configuration includes a reference-solution fallback only for all-zero-correctness groups during calibration; after initialization, all models use the standard GRPO objective without extra trainable parameters or loss changes. We also study Degenerate-Group Reflection Resampling (DGRR) as an optional extension that resamples all-zero-correctness groups after self-reflection without exposing reference solutions. Across Qwen2.5, Phi-3.5, and Gemma-2 backbones on GSM8K and MATH500, GRAIL consistently improves LoRA-based GRPO, with particularly strong gains on smaller Qwen and Gemma models. Analyses attribute these gains to stronger GRPO-gradient capture, smaller principal angles, and better handling of correctness-degenerate groups.

Speech large language models (Speech LLMs) are increasingly expected to reason in everyday spoken interactions, where users often revise task conditions through self-correction. Unlike ordinary disfluencies, self-corrections alter the premise structure of a problem: obsolete conditions must be discarded, while final corrected conditions must guide reasoning. We formulate this setting as self-corrected speech reasoning and study it as a condition-update problem. We construct SCUR-Bench (Spoken Condition-Update Reasoning Benchmark), a controlled Chinese benchmark of 13,295 instances organized by reasoning difficulty and self-correction difficulty, and introduce a three-path diagnostic protocol to analyze speech-side recovery, condition use, and reasoning. Our analysis reveals a recurrent failure pattern in current Speech LLMs: corrected conditions may be perceived, transcribed, or even mentioned, yet still fail to serve as active premises in reasoning. We term this final-condition adoption failure. A controlled English parallel evaluation exhibits the same recovery–adoption gap, providing preliminary evidence that this failure is not unique to Chinese. To mitigate it, we propose PACER, a perception-aware condition-enhanced reinforcement framework based on GRPO. On Qwen2.5-Omni-7B, PACER reduces end-to-end error and condition-related errors by 39.8% and 67.5%, respectively, relative to the untrained baseline.