# A KL Lens on Quantization: Fast, Forward-Only Sensitivity for Mixed-Precision SSM-Transformer Models

arXiv: https://arxiv.org/abs/2604.13440 · HTML: https://mlsanity.com/paper/2604.13440/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [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)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Zamba: A Compact 7B SSM Hybrid Model](https://mlsanity.com/paper/2405.16712/) (2024)
- [Hymba: A Hybrid-head Architecture for Small Language Models](https://mlsanity.com/paper/2411.13676/) (2024)
- [A Practical Mixed Precision Algorithm for Post-Training Quantization](https://mlsanity.com/paper/2302.05397/) (2023)
- [Efficient Quantization Strategies for Latent Diffusion Models](https://mlsanity.com/paper/2312.05431/) (2023)
- [Softmax Bias Correction for Quantized Generative Models](https://mlsanity.com/paper/2309.01729/) (2023)
- [Mamba-PTQ: Outlier Channels in Recurrent Large Language Models](https://mlsanity.com/paper/2407.12397/) (2024)
- [XAMBA: Enabling Efficient State Space Models on Resource-Constrained Neural Processing Units](https://mlsanity.com/paper/2502.06924/) (2025)
- [QMC: Efficient SLM Edge Inference via Outlier-Aware Quantization and Emergent Memories Co-Design](https://mlsanity.com/paper/2601.14549/) (2026)

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

- [REAL-Q: E2E LLM Quantization via Dynamic Gradient Descent](https://mlsanity.com/paper/2609.00049/) (2026)
- [Context-Aware Precision Scheduling for Small Language Models](https://mlsanity.com/paper/2610.15640/) (2026)

## Abstract (arXiv)

Deploying Large Language Models (LLMs) on edge devices faces severe computational and memory constraints, limiting real-time processing and on-device intelligence. Hybrid architectures combining Structured State Space Models (SSMs) with transformer-based LLMs offer a balance of efficiency and performance. Aggressive quantization can drastically cut model size and speed up inference, but its uneven effects on different components require careful management. In this work, we propose a lightweight, backpropagation-free, surrogate-based sensitivity analysis framework to identify hybrid SSM-Transformer components most susceptible to quantization-induced degradation. Relying solely on forward-pass metrics, our method avoids expensive gradient computations and retraining, making it suitable for situations where access to in-domain data is limited due to proprietary restrictions or privacy constraints. We also provide a formal analysis showing that the Kullback-Leibler (KL) divergence metric better captures quantization sensitivity for Language modeling tasks than widely adopted alternatives such as mean squared error (MSE) and signal-to-quantization-noise ratio (SQNR). Through extensive experiments on SSM and hybrid architectures, our ablation studies confirm that KL-based rankings align with observed performance drops and outperform alternative metrics. This framework enables the practical deployment of advanced hybrid models on resource-constrained edge devices with minimal accuracy loss. We further validate our approach with real-world on-device profiling on Intel Lunar Lake hardware, demonstrating that KL-guided mixed-precision achieves near-FP16 perplexity with model sizes and throughput competitive with Uniform INT4 on both CPU and GPU execution modes. Code is available at https://github.com/jasonkongie/kl-ssm-quant.