Quantizing Time-Series Models As Dynamical Systems: Trajectory-Based Quantization Sensitivity Score

2026-06-11

AI Summary

This work addresses the performance degradation of time series models in post-training quantization (PTQ), which arises from error propagation and amplification during quantization—particularly challenging in calibration-free or black-box settings where module sensitivity is hard to assess. To tackle this, the paper introduces discrete-time dynamical systems theory into quantization analysis for the first time. By modeling the inference process as a dynamical system, it proposes TQS, a quantizer-agnostic, prior-based sensitivity metric derived from trajectory sensitivity analysis, enabling calibration-free mixed-precision quantization budget allocation. The resulting TQS-PTQ framework significantly outperforms existing PTQ methods without relying on calibration data or second-order approximations, facilitating efficient low-bit deployment.

Abstract

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.

Problem

• post-training quantization
• time-series models
• quantization sensitivity
• dynamical systems
• error propagation

Innovation

• Trajectory-based Quantization Sensitivity Score
• Post-training Quantization
• Dynamical Systems
• Mixed-precision Quantization
• Quantization Error Propagation