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

TL;DR

Formula-R1 introduces a reinforcement learning approach that trains large language models to generate executable spreadsheet formulas, significantly improving their ability to perform complex numerical reasoning over tables.

Contribution

The paper presents Formula Tuning, a novel RL framework that enables LLMs to generate formulas for table reasoning without requiring supervised formula annotations.

Findings

Substantial performance improvements on seven table reasoning benchmarks.

Enhanced accuracy in complex, multi-step numerical reasoning tasks.

Outperforms prior methods in controlled experiments.

Abstract

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.