# TableMind++: An Uncertainty-Aware Programmatic Agent for Tool-Augmented Table Reasoning

arXiv: https://arxiv.org/abs/2603.07528 · HTML: https://mlsanity.com/paper/2603.07528/

## Key facts

- Cited by 1 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 44 of its 76 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 44)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [TAPAS: Weakly Supervised Table Parsing via Pre-training](https://mlsanity.com/paper/2004.02349/) (2020)
- [TabFact: A Large-scale Dataset for Table-based Fact Verification](https://mlsanity.com/paper/1909.02164/) (2019)
- [Understanding the planning of LLM agents: A survey](https://mlsanity.com/paper/2402.02716/) (2024)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [TAPEX: Table Pre-training via Learning a Neural SQL Executor](https://mlsanity.com/paper/2107.07653/) (2021)
- [ConvFinQA: Exploring the Chain of Numerical Reasoning in Conversational Finance Question Answering](https://mlsanity.com/paper/2210.03849/) (2022)
- [Plan-and-Act: Improving Planning of Agents for Long-Horizon Tasks](https://mlsanity.com/paper/2503.09572/) (2025)
- [Chain-of-Table: Evolving Tables in the Reasoning Chain for Table Understanding](https://mlsanity.com/paper/2401.04398/) (2024)
- [TableLlama: Towards Open Large Generalist Models for Tables](https://mlsanity.com/paper/2311.09206/) (2023)
- [emrQA: A Large Corpus for Question Answering on Electronic Medical Records](https://mlsanity.com/paper/1809.00732/) (2018)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [HiTab: A Hierarchical Table Dataset for Question Answering and Natural Language Generation](https://mlsanity.com/paper/2108.06712/) (2021)
- [BERT: A Review of Applications in Natural Language Processing and Understanding](https://mlsanity.com/paper/2103.11943/) (2021)
- [TableLLM: Enabling Tabular Data Manipulation by LLMs in Real Office Usage Scenarios](https://mlsanity.com/paper/2403.19318/) (2024)
- [TableGPT2: A Large Multimodal Model with Tabular Data Integration](https://mlsanity.com/paper/2411.02059/) (2024)
- [TableGPT: Towards Unifying Tables, Nature Language and Commands into One GPT](https://mlsanity.com/paper/2307.08674/) (2023)
- [Tab-CoT: Zero-shot Tabular Chain of Thought](https://mlsanity.com/paper/2305.17812/) (2023)

## Built on by (most cited first, 1 of 1)

- [TabClaw: An Interactive and Self-Evolving Agent for Spreadsheet Manipulation and Table Reasoning](https://mlsanity.com/paper/2606.10316/) (2026)

## Abstract (arXiv)

Table reasoning requires models to jointly perform semantic understanding and precise numerical operations. Most existing methods rely on a single-turn reasoning paradigm over tables which suffers from context overflow and weak numerical sensitivity. To address these limitations, we previously proposed TableMind as a tuning-based autonomous programmatic agent that simulates human-like interaction within a lightweight large language model (LLM). TableMind internalizes planning, action, and reflection through a two-stage training strategy involving supervised fine-tuning (SFT) on filtered high-quality data and reinforcement learning (RL) via a multi-perspective reward and the Rank-Aware Policy Optimization (RAPO) algorithm. While TableMind establishes a solid foundation for programmatic agents, the inherent stochasticity of LLMs remains a critical challenge that leads to hallucinations. In this paper, we extend this foundation to TableMind++ by introducing a novel uncertainty-aware inference framework to mitigate hallucinations. Specifically, we propose memory-guided plan pruning to retrieve historical trajectories for validating and filtering out logically flawed plans to address epistemic uncertainty. To ensure execution precision, we introduce confidence-based action refinement which monitors token-level probabilities to detect and self-correct syntactic noise for aleatoric uncertainty mitigation. Finally, we employ dual-weighted trajectory aggregation to synthesize a robust consensus from multiple reasoning paths. Extensive experiments on diverse benchmarks demonstrate that TableMind++ consistently outperforms previous baselines and proprietary models to validate the effectiveness of integrating autonomous training with uncertainty quantification. Our code is available.