# Formula-R1: Incentivizing LLM Reasoning over Complex Tables with Numerical Computation via Formula-Driven Reinforcement Learning

arXiv: https://arxiv.org/abs/2505.23667 · HTML: https://mlsanity.com/paper/2505.23667/

## Key facts

- Cited by 3 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 64 of its 83 references that are in the map.
- First posted on arXiv 29 May 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 64)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [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)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)

## Built on by (most cited first, 3 of 3)

- [Beyond Rows to Reasoning: Agentic Retrieval for Multimodal Spreadsheet Understanding and Editing](https://mlsanity.com/paper/2603.06503/) (2026)
- [MedGuideX: Internalizing Decision Logic from Executable Guidelines into Large Language Models for Clinical Reasoning](https://mlsanity.com/paper/2605.26567/) (2026)
- [MedRouter: Demystifying Knowledge Differences Across Medical LLMs for Routing-Based Reasoning](https://mlsanity.com/paper/2609.33119/) (2026)

## Abstract (arXiv)

Tables are a fundamental medium for organizing and analyzing data, making table reasoning a critical capability for intelligent systems. Although large language models (LLMs) exhibit strong general reasoning abilities, they still struggle with accurate numerical reasoning over tabular data, particularly in complex table settings beyond simple relational lookup. Spreadsheet formulas provide a powerful and expressive interface for executable symbolic operations, enabling rich reasoning patterns that remain largely underexplored by existing LLMs. In this paper, we introduce Formula-R1, a model trained via Formula Tuning (Fortune), a formula-driven reinforcement learning (RL) framework for table reasoning. Formula Tuning trains LLMs to generate executable spreadsheet formulas for question answering over general tabular data, using execution success and answer correctness as reward signals, thereby reducing reliance on supervised formula annotations. We demonstrate the effectiveness of Formula Tuning through extensive experiments on seven table reasoning benchmarks. It substantially improves LLM performance on table reasoning, particularly for tasks involving complex tables and multi-step numerical computation. Moreover, Formula-R1 consistently outperforms prior methods under controlled comparison settings. Beyond empirical gains, our extensive analyses provide insights into the role of RL in formula-driven table reasoning, highlighting the broader potential of formula-driven RL to enhance reasoning capabilities in LLMs.