# Table-r1: Self-supervised and Reinforcement Learning for Program-based Table Reasoning in Small Language Models

arXiv: https://arxiv.org/abs/2506.06137 · HTML: https://mlsanity.com/paper/2506.06137/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Chain-of-Table: Evolving Tables in the Reasoning Chain for Table Understanding](https://mlsanity.com/paper/2401.04398/) (2024)
- [Continual Learning for Large Language Models: A Survey](https://mlsanity.com/paper/2402.01364/) (2024)
- [Marco-o1: Towards Open Reasoning Models for Open-Ended Solutions](https://mlsanity.com/paper/2411.14405/) (2024)
- [Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning](https://mlsanity.com/paper/2402.13669/) (2024)
- [TroVE: Inducing Verifiable and Efficient Toolboxes for Solving Programmatic Tasks](https://mlsanity.com/paper/2401.12869/) (2024)
- [TableGPT2: A Large Multimodal Model with Tabular Data Integration](https://mlsanity.com/paper/2411.02059/) (2024)
- [Table-GPT: Table-tuned GPT for Diverse Table Tasks](https://mlsanity.com/paper/2310.09263/) (2023)
- [Large Language Model for Table Processing: A Survey](https://mlsanity.com/paper/2402.05121/) (2024)
- [Rethinking Tabular Data Understanding with Large Language Models](https://mlsanity.com/paper/2312.16702/) (2023)
- [Table-Critic: A Multi-Agent Framework for Collaborative Criticism and Refinement in Table Reasoning](https://mlsanity.com/paper/2502.11799/) (2025)
- [A Survey of Table Reasoning with Large Language Models](https://mlsanity.com/paper/2402.08259/) (2024)
- [StructLM: Towards Building Generalist Models for Structured Knowledge Grounding](https://mlsanity.com/paper/2402.16671/) (2024)
- [Towards Reasoning Ability of Small Language Models](https://mlsanity.com/paper/2502.11569/) (2025)
- [Large Language Models are Complex Table Parsers](https://mlsanity.com/paper/2312.11521/) (2023)
- [Tree-of-Table: Unleashing the Power of LLMs for Enhanced Large-Scale Table Understanding](https://mlsanity.com/paper/2411.08516/) (2024)
- [TableMaster: A Recipe to Advance Table Understanding with Language Models](https://mlsanity.com/paper/2501.19378/) (2025)
- [PoTable: Towards Systematic Thinking via Plan-then-Execute Stage Reasoning on Tables](https://mlsanity.com/paper/2412.04272/) (2024)

## Built on by (most cited first, 7 of 7)

- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [TaTToo: Tool-Grounded Thinking PRM for Test-Time Scaling in Tabular Reasoning](https://mlsanity.com/paper/2510.06217/) (2025)
- [STaR: Towards Effective and Stable Table Reasoning via Slow-Thinking Large Language Models](https://mlsanity.com/paper/2511.11233/) (2025)
- [Towards Robust Real-World Spreadsheet Understanding with Multi-Agent Multi-Format Reasoning](https://mlsanity.com/paper/2604.12282/) (2026)
- [JT-DA: Enhancing Data Analysis with Tool-Integrated Table Reasoning Large Language Models](https://mlsanity.com/paper/2512.06859/) (2025)
- [Replacing Multi-Step Assembly of Data Preparation Pipelines with One-Step LLM Pipeline Generation for Table QA](https://mlsanity.com/paper/2602.22721/) (2026)
- [Rethinking Stepwise Model Routing: A Cost-Efficient Table Reasoning Perspective](https://mlsanity.com/paper/2605.29319/) (2026)

## Abstract (arXiv)

Table reasoning (TR) requires structured reasoning over semi-structured tabular data and remains challenging, particularly for small language models (SLMs, e.g., LLaMA-8B) due to their limited capacity compared to large LMs (LLMs, e.g., GPT-4o). To narrow this gap, we explore program-based TR (P-TR), which circumvents key limitations of text-based TR (T-TR), notably in numerical reasoning, by generating executable programs. However, applying P-TR to SLMs introduces two challenges: (i) vulnerability to heterogeneity in table layouts, and (ii) inconsistency in reasoning due to limited code generation capability. We propose Table-r1, a two-stage P-TR method designed for SLMs. Stage 1 introduces an innovative self-supervised learning task, Layout Transformation Inference, to improve tabular layout generalization from a programmatic view. Stage 2 adopts a mix-paradigm variant of Group Relative Policy Optimization, enhancing P-TR consistency while allowing dynamic fallback to T-TR when needed. Experiments on four TR benchmarks demonstrate that Table-r1 outperforms all SLM-based methods, achieving at least a 15% accuracy improvement over the base model (LLaMA-8B) across all datasets and reaching performance competitive with LLMs.