Quantization Meets Reasoning: Exploring and Mitigating Degradation of Low-Bit LLMs in Mathematical Reasoning

Low-bit post-training quantization (PTQ) is a practical route to deploy reasoning-capable LLMs under tight memory and latency budgets, yet it can markedly impair mathematical reasoning (drops up to 69.81% in our harder settings). We address two deployment-critical questions with process-level precision: Where along a step-structured solution does degradation first arise? How to mitigate it while staying in the low-bit regime? Across widely used PTQ methods (AWQ, GPTQ, SmoothQuant), open-source model families (Qwen, LLaMA; 0.5--7B), and math reasoning benchmarks (GSM8K, MATH, AIME), we perform format-aligned chain-of-thought with step-aligned attribution and uncover two robust regularities: (i) PTQ disproportionately elevates method and execution errors relative to high-level conceptual mistakes; and (ii) failures emerge early, with the first vulnerable step flipping and cascading to the final answer. These regularities suggest a general intervention principle: restore local token-level margins exactly at the earliest failure frontier. We instantiate this principle as a lightweight measure$\rightarrow$locate$\rightarrow$restore loop that operates directly on the quantized model: detect the first faulty step, construct our "Silver Bullet" datasets, and apply small-scale supervised/preference tuning. In our settings, as few as 332 curated examples and 3--5 minutes of compute on a single GPU recover 4-bit weight math reasoning toward the full-precision baseline while preserving PTQ efficiency. Our framework is quantizer- and architecture-agnostic within the evaluated regimes, and turns low-bit degradation from a global accuracy problem into a local, reproducible process intervention.