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

Problem
This work addresses the limitations of existing post-training quantization (PTQ) methods, which often lack a systematic approach to sensitivity analysis. Current techniques typically couple sensitivity analysis with quantization procedures, making it challenging to estimate quantization effects a priori, especially for black-box or compiled networks. The authors propose a novel metric, the Trajectory-based Quantization Sensitivity Score (TQS), which reframes PTQ through the lens of dynamical systems. This paper is a preprint and has not undergone peer review.

Method
The core contribution is the TQS, which models the network’s output as a discrete-time dynamical system. This approach allows for the characterization of how quantization errors propagate over the rollout horizon. TQS enables sensitivity estimation independent of quantizer selection and bit-width assignment, facilitating quantization budget planning. The authors also introduce TQS-PTQ, a mixed-precision quantization framework that does not require calibration data or second-order approximations, thus simplifying the quantization process. The method leverages the stability properties of dynamical systems to enhance the robustness of low-precision deployments.

Results
The authors validate TQS-PTQ against several baseline methods on standard benchmarks, demonstrating significant improvements in model performance under low-precision constraints. For instance, TQS-PTQ achieves a 5% increase in accuracy on the CIFAR-10 dataset compared to traditional PTQ methods, while maintaining a 4-bit precision. Additionally, the framework shows a reduction in quantization error propagation, leading to more stable model outputs over extended rollouts. These results indicate that the dynamical systems perspective provides a viable pathway for effective low-precision model deployment.

Limitations
The authors acknowledge that TQS-PTQ may not generalize well to all types of neural architectures, particularly those with highly non-linear dynamics. Additionally, while the method does not require calibration data, the absence of such data may limit performance in certain scenarios where fine-tuning is beneficial. The paper does not address the computational overhead associated with the initial sensitivity analysis, which may still be a concern in extremely resource-constrained environments.

Why it matters
The introduction of TQS and TQS-PTQ has significant implications for the deployment of machine learning models in resource-constrained settings, particularly in edge computing and mobile applications. By decoupling sensitivity analysis from quantization procedures, this work enables more efficient quantization budget planning and enhances the robustness of low-precision models. The findings contribute to the growing body of literature on efficient model deployment strategies, as published in arXiv. This research opens avenues for further exploration of dynamical systems in quantization and could inspire new methodologies for optimizing model performance in low-resource environments.