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

arXiv: https://arxiv.org/abs/2606.13300 · HTML: https://mlsanity.com/paper/2606.13300/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [GPTAQ: Efficient Finetuning-Free Quantization for Asymmetric Calibration](https://mlsanity.com/paper/2504.02692/) (2025)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [On Lyapunov Exponents for RNNs: Understanding Information Propagation Using Dynamical Systems Tools](https://mlsanity.com/paper/2006.14123/) (2020)
- [Finite-time Lyapunov exponents of deep neural networks](https://mlsanity.com/paper/2306.12548/) (2023)
- [Identifying Sensitive Weights via Post-quantization Integral](https://mlsanity.com/paper/2503.01901/) (2025)
- [Mix-QViT: Mixed-Precision Vision Transformer Quantization Driven by Layer Importance and Quantization Sensitivity](https://mlsanity.com/paper/2501.06357/) (2025)

## Built on by (most cited first, 2 of 2)

- [Auditing Invisible Weight Updates with Reference Traces](https://mlsanity.com/paper/2607.09800/) (2026)
- [Calibration Bets on the Past: Post-Training Quantization for Financial Time-Series Forecasting](https://mlsanity.com/paper/2608.12259/) (2026)

## Abstract (arXiv)

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.