# RATIO: Reasoning Analysis and Token-level Inference Optimization for Quantized Reasoning Models

arXiv: https://arxiv.org/abs/2609.39801 · HTML: https://mlsanity.com/paper/2609.39801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

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- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Quantization Meets Reasoning: Exploring LLM Low-Bit Quantization Degradation for Mathematical Reasoning](https://mlsanity.com/paper/2501.03035/) (2025)
- [RaZeR: Pushing the Limits of NVFP4 Quantization with Redundant Zero Remapping](https://mlsanity.com/paper/2501.04052/) (2025)
- [QuantLRM: Quantization of Large Reasoning Models via Fine-Tuning Signals](https://mlsanity.com/paper/2602.02581/) (2026)
- [SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization](https://mlsanity.com/paper/2605.12245/) (2026)
- [FOCUS: FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling](https://mlsanity.com/paper/2608.01847/) (2026)
- [Extreme Low-Bit Inference in Reasoning Models: Failure Modes and Targeted Recovery](https://mlsanity.com/paper/2606.02011/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) has become a widely adopted technique for reducing the memory footprint and inference cost of large language models (LLMs). However, recent studies reveal that when applied to reasoning models, PTQ not only degrades reasoning performance but also exacerbates overthinking, leading to longer reasoning trajectories. These issues may offset the efficiency gains expected from lower-precision inference. Existing approaches mainly rely on complex optimization procedures. More recent lightweight inference strategies instead use predefined overthinking markers, limiting their adaptability across quantized models. To address these issues, we propose Reasoning Analysis and Token-level Inference Optimization (RATIO), a framework that identifies model-specific overthinking tokens and assigns each a tailored penalty. RATIO first introduces Quantization-aware Reasoning Behavior Analysis (QRBA) to identify overthinking tokens by analyzing discrepancies between full-precision and quantized models. It then adopts Token-Specific Penalty Determination (TSPD), which leverages full-precision guidance to derive token-specific penalties without additional training. Extensive experiments show that RATIO achieves a better accuracy-efficiency trade-off than existing token-level interventions. Specifically, RATIO achieves up to 9.8 points accuracy improvement and reduces chain-of-thought (CoT) length by up to 51.3% compared with quantized baselines. The code will be available at https://github.com/steven-bao1/RATIO.