Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning, yet merging multiple task-specific LoRA updates without additional training remains challenging. Most existing LoRA merging methods rely on SVD-based alignment, which emphasizes globally shared structure across tasks. In this work, we show that LoRA merging performance can be further improved by combining SVD with CUR decomposition. Through a representation-level analysis, we find that SVD-based decompositions primarily model shared components across tasks, while CUR-based decompositions better preserve task-specific and localized updates. These two perspectives are geometrically misaligned and exhibit complementary advantages, revealing an inherent trade-off between capturing shared structure and preserving task-specific information in LoRA model merging. Guided by this analysis, we propose a training-free merging procedure that explicitly combines the shared structure captured by SVD with the task-specific components preserved by CUR. Experiments on both vision and language benchmarks demonstrate consistent improvements over existing gradient-free LoRA merging methods.

While Chain-of-Thought (CoT) reasoning enhances code generation in Large Language Models (LLMs), it introduces a critical challenge in uncertainty estimation: Confidence Saturation. Existing calibration methods, such as Self-Consistency, rely on the assumption that consensus implies correctness. This assumption fails under systematic errors, where models confidently repeat flawed logic, leading to miscalibrated high-confidence predictions. To address this, we introduce NeuroSym-Cal, a hierarchical calibration framework. We posit that reliable confidence requires interrogating the model at two complementary levels: the extrinsic consensus of its symbolic outputs and the intrinsic sensitivity of its latent reasoning. Specifically, we propose Reasoning Sensitivity Analysis to measure the local curvature of the deductive process via latent perturbation, providing a fine-grained signal that persists even when output consensus saturates. These orthogonal features are fused by a Contextual Calibration Network to predict correctness. Experiments across state-of-the-art reasoning models (e.g., DeepSeek-R1) demonstrate that NeuroSym-Cal effectively de-saturates overconfident errors, achieving state-of-the-art Expected Calibration Error (ECE) and superior selective generation performance on Out-Of-Domain (OOD) benchmarks.