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

Dong Jin; Jian Yang; Shenghao Ye; Shuangwu Chen; Yu Guo; Yuxiang Wang

arxiv: 2605.29319 · v1 · pith:RKPCLWTRnew · submitted 2026-05-28 · 💻 cs.CL

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

Shenghao Ye , Yuxiang Wang , Yu Guo , Dong Jin , Shuangwu Chen , Jian Yang This is my paper

Pith reviewed 2026-06-29 07:45 UTC · model grok-4.3

classification 💻 cs.CL

keywords table reasoningstepwise model routinguncertainty estimationefficient inferencelarge reasoning modelstoken uncertaintyrouting framework

0 comments

The pith

EcoTab routes table reasoning steps by separately estimating uncertainties of table tokens and text tokens to decide when to use smaller models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that table reasoning steps mix two token types with different uncertainty patterns: table tokens tied to structure like cell values and headers, and text tokens in the surrounding natural language. Both types of uncertainty predict the chance the model will err on the next step, yet prior routing methods treat all tokens the same and therefore make suboptimal choices about when to hand off to a smaller model. EcoTab addresses this by estimating the two uncertainties independently at every step, converting each into a failure risk for the small model, and combining the risks to make the routing call. Experiments across table reasoning benchmarks indicate this produces higher accuracy at lower total cost than strong baselines. A reader would care because long traces from large reasoning models are expensive, and the work demonstrates how the internal structure of table tasks can be used to reduce that expense without changing the models themselves.

Core claim

In table reasoning traces, table tokens and text tokens exhibit distinct uncertainty distributions, and the uncertainty of each type correlates with the risk that the small model will produce an error in the subsequent reasoning step. Existing stepwise routing does not model the two types separately and therefore yields suboptimal routing decisions. EcoTab corrects this by estimating the uncertainties of table tokens and text tokens independently, mapping each estimate to a next-step failure risk for the small model, and using the combined risks to choose the model for the current step.

What carries the argument

EcoTab, a table-aware stepwise routing framework that separately estimates uncertainties of table tokens and text tokens, maps each to next-step failure risk for the small model, and combines the two risks to decide routing.

If this is right

EcoTab consistently outperforms strong baselines on multiple table reasoning benchmarks.
EcoTab achieves a better accuracy-efficiency balance than existing stepwise routing methods for table tasks.
Separately modeling table-token and text-token uncertainties improves routing decisions over methods that treat all tokens uniformly.
The uncertainty of both token types correlates with next-step error risk, enabling more precise risk mapping for the small model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same separation of structured versus unstructured token uncertainties could be tested on related tasks such as code generation or symbolic math to see whether similar cost savings appear.
Routing systems built on EcoTab could be combined with existing model-compression methods to compound efficiency gains beyond routing alone.
Automatic detection of token-type boundaries during generation might remove the need for task-specific table identification in future versions.

Load-bearing premise

That separately estimating uncertainties for table tokens and text tokens and mapping them to next-step failure risks will produce better routing decisions than methods that do not separate the token types.

What would settle it

A head-to-head experiment in which a stepwise router that does not separate table-token and text-token uncertainties matches or exceeds EcoTab's accuracy at equal or lower total inference cost on the same benchmarks would falsify the advantage of the separation step.

Figures

Figures reproduced from arXiv: 2605.29319 by Dong Jin, Jian Yang, Shenghao Ye, Shuangwu Chen, Yu Guo, Yuxiang Wang.

**Figure 2.** Figure 2: Error distribution across four step categories [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: (Left) Difference in average entropy between [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 5.** Figure 5: Overview of the EcoTab framework. By separately modeling table tokens and text tokens in each reasoning [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

**Figure 6.** Figure 6: Failure-risk mapping transferability of EcoTab. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 8.** Figure 8: LRM usage rate across GPT-5.4-High diffi [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: Overall routing latency on TableBench, to [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: Table Retrieval case with SRM-only [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 12.** Figure 12: Table Operation case with EcoTab. Case Study on EcoTab (2) Table Operation (i) SRM-only Fail [Step 1] Okay, let's see. The user is asking if the dates in the table are set in a consecutive order. Let me look at the dates provided. [Step 2] First, I need to list out all the dates from the table. Let me check each row:1. 16 May 20102. 13 February 20113. 7 August 20114. 6 November 20115. 20 November 20116. 2… view at source ↗

**Figure 11.** Figure 11: Table Retrieval case with STEER. Case Study on EcoTab (1) Table Retrieval (iii) EcoTab Correct [Step 1] Okay, let's see. The question is asking for the number of times Electrodyne won in the 1984 IMSA GT Championship season. [Step 2] First, I need to look at the table provided and check the "GTO Winning Team" column, because that's where Electrodyne is mentioned. The GTO stands for Group Toyota, but in th… view at source ↗

**Figure 13.** Figure 13: Table Operation case with SRM-only [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗

**Figure 14.** Figure 14: Table Operation case with STEER. Case Study on EcoTab (2) Table Operation (iii) EcoTab Correct [Step 1] Okay, let's see. The user is asking if the dates in the table are set in a consecutive order. Let me check the dates provided. [Step 2] Looking at the table, the dates are: 16 May 2010, 13 February 2011, 7 August 2011, 6 November 2011, 20 November 2011, 23 January 2012, 30 January 2012, 17 September 201… view at source ↗

**Figure 15.** Figure 15: Table Operation case with EcoTab [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

EcoTab splits uncertainty estimation between table tokens and text tokens for stepwise routing, but the abstract shows no numbers or setup so the performance claims cannot be checked.

read the letter

The main point your colleague needs to hear is that the paper identifies distinct uncertainty patterns for table tokens versus text tokens in reasoning steps, and proposes to use that split to make better routing decisions between small and large models. The abstract does not include any actual performance numbers or experimental setup, so we cannot tell yet if the approach delivers on its claims.

What is new is the focus on table reasoning as a specific case for stepwise routing. The authors observe that table tokens (cell values, headers) and text tokens have separate uncertainty distributions, and both link to the chance the small model will fail on the next step. They then build EcoTab to estimate each separately, convert to risk scores, and combine them for the routing choice. This seems like a logical specialization of general stepwise routing methods.

The work does well at making the case for why treating all tokens the same might be suboptimal here. The empirical analysis mentioned in the abstract sounds like it could be useful for people who run table tasks often, since those tasks show up in data analysis and business apps.

The soft spots are in the evidence. The abstract asserts outperformance on benchmarks and a better accuracy-efficiency trade-off, but supplies no quantitative results, baseline names, statistical tests, or error analysis. The full experimental details are missing from what we have. That makes it hard to judge soundness. The central assumption—that separate modeling will produce better decisions—might hold, but we need the data to check.

This paper is aimed at people working on cost-efficient LLM inference for structured reasoning tasks. A reader who cares about practical efficiency gains in table-heavy applications could find the routing idea worth trying, even if the current description is thin.

It deserves a serious referee because the idea is falsifiable through benchmark comparisons and addresses a real deployment issue. The stress test found no internal contradictions in the described pipeline.

I would recommend sending it to peer review so the experiments can be evaluated properly.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes EcoTab, a table-aware stepwise model routing framework for efficient table reasoning with large reasoning models (LRMs). Through empirical analysis, it identifies that reasoning steps contain table tokens (grounded in table structure) and text tokens (natural-language reasoning) with distinct uncertainty distributions, both correlated with next-step failure risk for smaller models. Existing stepwise routing methods are argued to be suboptimal because they do not model these token types separately. EcoTab estimates the uncertainties separately, maps each to next-step failure risks, and combines them for routing decisions. Experiments on multiple table reasoning benchmarks are claimed to show that EcoTab consistently outperforms strong baselines while achieving a superior accuracy-efficiency tradeoff.

Significance. If the empirical correlations and routing improvements hold under proper validation, the work could provide a targeted refinement to uncertainty-based stepwise routing specifically for table reasoning tasks, potentially reducing inference costs for LRMs without accuracy loss. The approach is presented as directly falsifiable via benchmark experiments and grounded in observable token-type uncertainty differences rather than untestable theoretical assumptions.

major comments (2)

[Abstract / Experiments] Abstract and Experiments section: the central claim that 'EcoTab consistently outperforms strong baselines and achieves a better balance between accuracy and efficiency' is asserted without any quantitative results, baseline descriptions, statistical tests, error analysis, or even summary metrics; this absence is load-bearing because the entire contribution rests on the empirical demonstration of improved routing decisions.
[Method / EcoTab framework] Method description (around the EcoTab framework): the procedure for separately estimating uncertainties of table tokens versus text tokens, mapping each to next-step failure risks for the small model, and combining the risks is described only at a high level with no equations, algorithms, or implementation details; without these, it is impossible to assess whether the separation actually yields better decisions than non-separated baselines or to reproduce the claimed improvements.

minor comments (2)

[Abstract / Title] The abstract and title could more explicitly indicate the scope (table reasoning only) to avoid overgeneralization to general stepwise routing.
[Introduction / Preliminaries] Notation for 'table tokens' and 'text tokens' should be defined with examples or a figure early in the paper for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which identify key areas where additional detail will strengthen the manuscript. We will revise the paper to provide quantitative empirical support and fuller methodological specifications while preserving the core contributions.

read point-by-point responses

Referee: [Abstract / Experiments] Abstract and Experiments section: the central claim that 'EcoTab consistently outperforms strong baselines and achieves a better balance between accuracy and efficiency' is asserted without any quantitative results, baseline descriptions, statistical tests, error analysis, or even summary metrics; this absence is load-bearing because the entire contribution rests on the empirical demonstration of improved routing decisions.

Authors: We agree that the abstract and experiments section would be strengthened by explicit quantitative support. In the revision we will insert a concise summary of key metrics (accuracy, cost reduction, and efficiency-accuracy trade-off) directly into the abstract, expand the experiments section with baseline descriptions, tabulated results across all benchmarks, statistical significance tests, and a short error analysis. These additions will make the empirical claims verifiable without altering the underlying findings. revision: yes
Referee: [Method / EcoTab framework] Method description (around the EcoTab framework): the procedure for separately estimating uncertainties of table tokens versus text tokens, mapping each to next-step failure risks for the small model, and combining the risks is described only at a high level with no equations, algorithms, or implementation details; without these, it is impossible to assess whether the separation actually yields better decisions than non-separated baselines or to reproduce the claimed improvements.

Authors: We accept that the current description is insufficiently detailed for reproduction and evaluation. The revised manuscript will add explicit equations for per-token-type uncertainty estimation, the risk-mapping functions, and the risk-combination rule; we will also include a pseudocode algorithm and concrete implementation parameters (e.g., token classification heuristics and risk-threshold calibration). These changes will allow direct comparison with non-separated baselines. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes an empirical pipeline: observe distinct uncertainty distributions for table tokens versus text tokens, correlate each with next-step failure risk, and route decisions on the combined signal. No equations, fitted parameters, or derivations are presented that reduce by construction to the inputs themselves. The method is falsifiable on external benchmarks and does not rely on self-citations or ansatzes that loop back to the target result. The central claim rests on observable correlations rather than self-referential definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.1-grok · 5738 in / 981 out tokens · 22092 ms · 2026-06-29T07:45:17.790225+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

9 extracted references · 4 canonical work pages · 2 internal anchors

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InProceedings of the 58th annual meet- ing of the association for computational linguistics, pages 4320–4333

Tapas: Weakly supervised table parsing via pre-training. InProceedings of the 58th annual meet- ing of the association for computational linguistics, pages 4320–4333. Hiroshi Iida, Dung Thai, Varun Manjunatha, and Mohit Iyyer. 2021. Tabbie: Pretrained representations of tabular data. InProceedings of the 2021 Conference of the North American Chapter of th...

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Fast inference from transformers via spec- ulative decoding. InInternational Conference on Machine Learning, pages 19274–19286. PMLR. Liyao Li, Chao Ye, Wentao Ye, Yifei Sun, Zhe Jiang, Haobo Wang, Jiaming Tian, Yiming Zhang, Ning- tao Wang, Xing Fu, and 1 others. 2025. Table as a modality for large language models.arXiv preprint arXiv:2512.00947. Baohao ...

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Let’s verify step by step.arXiv preprint arXiv:2305.20050. Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang, and Xinchao Wang. 2025. Cot-valve: Length- compressible chain-of-thought tuning. InProceed- ings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pa- pers), pages 6025–6035. Benjamin Newman, Yoonjoo Lee,...

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When TableQA Meets Noise: A Dual Denoising Framework for Complex Questions and Large-scale Tables

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work page internal anchor Pith review Pith/arXiv arXiv 2020
[6]

1,200” and “1200

for cross-family collaboration. This design allows us to evaluate whether EcoTab remains effective under both homogeneous and heteroge- neous model pairs. For EcoTab and all compared baselines, we use the same decoding configuration for fair comparison. Specifically, we set the tem- perature to 0.7, the maximum generation length to 16,384 tokens, and top-...

2015
[7]

Then 20 Nov 2011

Then 6 Nov 2011. Then 20 Nov 2011. Then 23 Jan

2011
[8]

Then 17 Sep 2012

Then 30 Jan 2012. Then 17 Sep 2012. Then 12 Nov

2012
[9]

[Step 5] Question: are the dates set in a consecutive order? Table: {table content} Answer: yes [Step 4] Wait, but between 20 Nov 2011 and 23 Jan 2012, there's a gap

Then 28 Oct 2013. [Step 5] Question: are the dates set in a consecutive order? Table: {table content} Answer: yes [Step 4] Wait, but between 20 Nov 2011 and 23 Jan 2012, there's a gap. Let me check the dates again. 20 Nov 2011, then 23 Jan 2012. That's a few months later. Then 30 Jan 2012, then 17 Sep 2012, then 12 Nov 2012, then 28 Oct 2013. So there's a...

2013

[1] [1]

InProceedings of the 58th annual meet- ing of the association for computational linguistics, pages 4320–4333

Tapas: Weakly supervised table parsing via pre-training. InProceedings of the 58th annual meet- ing of the association for computational linguistics, pages 4320–4333. Hiroshi Iida, Dung Thai, Varun Manjunatha, and Mohit Iyyer. 2021. Tabbie: Pretrained representations of tabular data. InProceedings of the 2021 Conference of the North American Chapter of th...

2021

[2] [2]

Rihui Jin, Zheyu Xin, Xing Xie, Zuoyi Li, Guilin Qi, Yongrui Chen, Xinbang Dai, Tongtong Wu, and Gho- lamreza Haffari

Springer. Rihui Jin, Zheyu Xin, Xing Xie, Zuoyi Li, Guilin Qi, Yongrui Chen, Xinbang Dai, Tongtong Wu, and Gho- lamreza Haffari. 2025. Table-r1: Self-supervised and reinforcement learning for program-based table reasoning in small language models.arXiv preprint arXiv:2506.06137. Sangmook Lee, Dohyung Kim, Hyukhun Koh, Nakyeong Yang, and Kyomin Jung. 2025....

work page arXiv 2025

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InInternational Conference on Machine Learning, pages 19274–19286

Fast inference from transformers via spec- ulative decoding. InInternational Conference on Machine Learning, pages 19274–19286. PMLR. Liyao Li, Chao Ye, Wentao Ye, Yifei Sun, Zhe Jiang, Haobo Wang, Jiaming Tian, Yiming Zhang, Ning- tao Wang, Xing Fu, and 1 others. 2025. Table as a modality for large language models.arXiv preprint arXiv:2512.00947. Baohao ...

work page arXiv 2025

[4] [4]

Let's Verify Step by Step

Let’s verify step by step.arXiv preprint arXiv:2305.20050. Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang, and Xinchao Wang. 2025. Cot-valve: Length- compressible chain-of-thought tuning. InProceed- ings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pa- pers), pages 6025–6035. Benjamin Newman, Yoonjoo Lee,...

work page internal anchor Pith review Pith/arXiv arXiv 2025

[5] [5]

When TableQA Meets Noise: A Dual Denoising Framework for Complex Questions and Large-scale Tables

When tableqa meets noise: A dual denoising framework for complex questions and large-scale tables.arXiv preprint arXiv:2509.17680. Pengcheng Yin, Graham Neubig, Wen-tau Yih, and Se- bastian Riedel. 2020. Tabert: Pretraining for joint understanding of textual and tabular data. InProceed- ings of the 58th annual meeting of the association for computational ...

work page internal anchor Pith review Pith/arXiv arXiv 2020

[6] [6]

1,200” and “1200

for cross-family collaboration. This design allows us to evaluate whether EcoTab remains effective under both homogeneous and heteroge- neous model pairs. For EcoTab and all compared baselines, we use the same decoding configuration for fair comparison. Specifically, we set the tem- perature to 0.7, the maximum generation length to 16,384 tokens, and top-...

2015

[7] [7]

Then 20 Nov 2011

Then 6 Nov 2011. Then 20 Nov 2011. Then 23 Jan

2011

[8] [8]

Then 17 Sep 2012

Then 30 Jan 2012. Then 17 Sep 2012. Then 12 Nov

2012

[9] [9]

[Step 5] Question: are the dates set in a consecutive order? Table: {table content} Answer: yes [Step 4] Wait, but between 20 Nov 2011 and 23 Jan 2012, there's a gap

Then 28 Oct 2013. [Step 5] Question: are the dates set in a consecutive order? Table: {table content} Answer: yes [Step 4] Wait, but between 20 Nov 2011 and 23 Jan 2012, there's a gap. Let me check the dates again. 20 Nov 2011, then 23 Jan 2012. That's a few months later. Then 30 Jan 2012, then 17 Sep 2012, then 12 Nov 2012, then 28 Oct 2013. So there's a...

2013