ReQOR: Operator-Discrepancy Subspace Repair for Quantization-Conditioned Backdoors in Large Language Models

Quantization-Conditioned Backdoors (QCBs) cause large language models (LLMs) to exhibit malicious behavior after quantization while remaining benign at high precision. Existing defenses often rely on security-guided configuration selection or iterative optimization, but do not identify which quantization-induced changes should be repaired. We isolate module-local quantization effects from upstream drift by evaluating the high-precision and quantized versions of each module on identical states from the quantized inference trajectory, and formulate QCB defense as repairing the resulting same-state operator discrepancies. We propose ReQOR, a training-free defense that identifies the dominant directions of these discrepancies on benign calibration data and restores the full-precision computation along them in closed form, yielding a factorized residual adapter. ReQOR uses neither attack information nor gradient-based optimization and supports both full-span and low-rank repair. Experiments across four LLMs, three QCB attacks, three malicious behaviors, and three quantization formats show substantial QCB mitigation while largely preserving benign utility. Further analysis shows that dominant operator-discrepancy directions provide more effective and rank-efficient repair than rank-matched random, low-energy, or raw weight-error directions, while low-rank ReQOR reduces deployment memory overhead.