Right On Q: Recovering Reasoning under Quantization via Self-Generated Trajectories

Boyuan Zheng, Jing Xiong, Chenwei Wu, Hui Shen, Zesen Zhao +6

Quantization-aware training (QAT) aims to recover reasoning capabilities in low-bit large language models (LLMs). Existing recipes typically supervise the quantized student with the original full-precision model on fixed response sequences. However, the resulting low-bit quantized models still struggle on long-horizon reasoning tasks and often fail to terminate within a token budget that suffices for the full-precision model. We identify two challenges in closing this gap. First, fixed-response supervision leaves a mismatch between training prefixes and those encountered during student generation, and this trajectory divergence grows as responses lengthen. Second, on its own prefixes, the student underpredicts some next-token candidates and overpredicts others, and this distributional misalignment becomes more frequent at high-entropy prefixes. We present OnQ, a low-bit recovery pipeline that combines on-policy distillation and candidate-wise Dynamic KL. Starting from block-wise calibration, the quantized student generates responses and receives full-precision teacher supervision on its own prefixes. Dynamic KL weights forward and reverse KL by each candidate's teacher-student…