# STEPQuant: When and Where Errors Matter in Delta-Rule Recurrent State Quantization

arXiv: https://arxiv.org/abs/2609.38169 · HTML: https://mlsanity.com/paper/2609.38169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache quantization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 54 of its 67 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache quantization](https://mlsanity.com/inference/kv-cache-quantization/)

## Builds on (most cited first, 30 of 54)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)

## Abstract (arXiv)

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.