# FormulaSPIN: Self-Play Fine-Tuning for Natural Language to Spreadsheet Formula Generation

arXiv: https://arxiv.org/abs/2607.19354 · HTML: https://mlsanity.com/paper/2607.19354/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-play RL for reasoning, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 18 of 18)

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- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [TAPEX: Table Pre-training via Learning a Neural SQL Executor](https://mlsanity.com/paper/2107.07653/) (2021)
- [TUTA: Tree-based Transformers for Generally Structured Table Pre-training](https://mlsanity.com/paper/2010.12537/) (2020)
- [TableFormer: Robust Transformer Modeling for Table-Text Encoding](https://mlsanity.com/paper/2203.00274/) (2022)
- [Curriculum Learning for Small Code Language Models](https://mlsanity.com/paper/2407.10194/) (2024)
- [FORTAP: Using Formulas for Numerical-Reasoning-Aware Table Pretraining](https://mlsanity.com/paper/2109.07323/) (2021)
- [SPFT-SQL: Enhancing Large Language Model for Text-to-SQL Parsing by Self-Play Fine-Tuning](https://mlsanity.com/paper/2509.03937/) (2025)

## Abstract (arXiv)

Spreadsheet applications are used by hundreds of millions worldwide, yet writing formulas remains a significant barrier. Existing approaches rely on static supervised data, which quickly saturates on limited annotations. In this paper, we introduce FORMULASPIN, a self-play framework that breaks the ceiling of supervised fine-tuning by enabling iterative self-improvement without any additional data. Vanilla SPIN fails on this task: it uniformly penalizes every non-matching output, so execution-equivalent alternatives are punished as negatives in one example while serving as ground truth in another, producing contradictory gradients. Our framework resolves this by exploiting formula generation's unique advantage: binary executability provides implicit supervision that separates semantic errors from valid stylistic variants. We frame training as a two-player game in which the main player learns to prefer ground-truth formulas over those from its previous version, while execution feedback sorts outputs into distinct granularities-enabling an adaptive curriculum that shifts from semantic correctness to stylistic refinement. To further increase accuracy, we incorporate ExecVote, a semantic-level voting mechanism that naturally handles multiple valid formulations. Experiments on multiple benchmarks demonstrate that FORMULASPIN achieves state-of-the-art performance, with 74.9% exact match and 87.1% execution accuracy on NL2FORMULA, matching models trained with additional preference annotations while outperforming both traditional SFT and frontier proprietary models. These findings underscore self-play's potential to tackle scarce data tasks and open the door to extending it beyond executable domains.