# Rethinking Stepwise Model Routing: A Cost-Efficient Table Reasoning Perspective

arXiv: https://arxiv.org/abs/2605.29319 · HTML: https://mlsanity.com/paper/2605.29319/

## 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 16 of its 48 references that are in the map.
- First posted on arXiv 28 May 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, 16 of 16)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [TableGPT2: A Large Multimodal Model with Tabular Data Integration](https://mlsanity.com/paper/2411.02059/) (2024)
- [VRAG-RL: Empower Vision-Perception-Based RAG for Visually Rich Information Understanding via Iterative Reasoning with Reinforcement Learning](https://mlsanity.com/paper/2505.22019/) (2025)
- [Table-R1: Region-based Reinforcement Learning for Table Understanding](https://mlsanity.com/paper/2505.12415/) (2025)
- [Understanding and Benchmarking Artificial Intelligence: OpenAI's o3 Is Not AGI](https://mlsanity.com/paper/2501.07458/) (2025)
- [GlimpRouter: Efficient Collaborative Inference by Glimpsing One Token of Thoughts](https://mlsanity.com/paper/2601.05110/) (2026)
- [When TableQA Meets Noise: A Dual Denoising Framework for Complex Questions and Large-scale Tables](https://mlsanity.com/paper/2509.17680/) (2025)
- [Confidence-Guided Stepwise Model Routing for Cost-Efficient Reasoning](https://mlsanity.com/paper/2511.06190/) (2025)
- [Table-r1: Self-supervised and Reinforcement Learning for Program-based Table Reasoning in Small Language Models](https://mlsanity.com/paper/2506.06137/) (2025)
- [Table as a Modality for Large Language Models](https://mlsanity.com/paper/2512.00947/) (2025)
- [Optimizing Reasoning Efficiency through Prompt Difficulty Prediction](https://mlsanity.com/paper/2511.03808/) (2025)

## Abstract (arXiv)

Large Reasoning Models (LRMs) achieve strong performance on table reasoning tasks but incur substantial inference cost due to long reasoning traces. Stepwise model routing mitigates this issue by dynamically assigning reasoning steps to smaller or larger models. However, stepwise model routing for table reasoning remains underexplored. Through empirical analysis, we find that reasoning steps involving tables contain two types of tokens with distinct uncertainty distributions: table tokens grounded in table structure, such as cell values and headers, and text tokens representing surrounding natural-language reasoning. The uncertainty of both token types is correlated with the risk that the model makes an error in the next reasoning step. However, existing methods fail to model them separately, leading to suboptimal routing decisions. To address this, we propose EcoTab, a table-aware stepwise routing framework for efficient table reasoning. At each reasoning step, EcoTab separately estimates the uncertainties of table tokens and text tokens, maps them to next-step failure risks for the small model, and combines the two risks for routing. Experiments on multiple table reasoning benchmarks show that EcoTab consistently outperforms strong baselines and achieves a better balance between accuracy and efficiency.