We introduce the Trajectory-based Quantization Sensitivity Score (TQS), a metric that reframes post-training quantization (PTQ) through the lens of dynamical-systems stability. By modeling the network's rollout as a discrete-time dynamical system, TQS characterizes how quantization-induced errors propagate and amplify over the rollout horizon. Unlike conventional PTQ methods, where sensitivity analysis is often coupled to the quantization procedure, TQS enables a priori sensitivity estimation decoupled from quantizer selection and bit-width assignment. This separation allows for quantization budget planning even for black-box or compiled networks with fused operators. Building on this, we present TQS-PTQ, a flexible mixed-precision framework that requires no calibration data or costly second-order approximations. Our experiments show that a dynamical-systems perspective provides a robust, high-performing pathway for low-precision deployment in resource-constrained settings.

翻译：我们提出了基于轨迹的量化和敏感度评分（TQS），这是一种通过动力学系统稳定性视角重新审视训练后量化（PTQ）的指标。通过将网络的前向传播建模为离散时间动力学系统，TQS刻画了量化误差如何在时域展开过程中传播并放大。与传统PTQ方法中敏感度分析通常与量化过程耦合不同，TQS能够实现与量化器选择和比特宽度分配解耦的先验敏感度估计。这种分离使得即使对于具有融合算子的黑盒或编译网络，也能进行量化预算规划。基于此，我们提出了TQS-PTQ，这是一种灵活的混合精度框架，无需校准数据或昂贵的二阶近似。实验表明，动力学系统视角为资源受限环境下的低精度部署提供了稳健且高性能的路径。