# Towards an AI Musician: Synthesizing Sheet Music Problems for Musical Reasoning

arXiv: https://arxiv.org/abs/2509.04059 · HTML: https://mlsanity.com/paper/2509.04059/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Audio-language model reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Placed in

- LLM reasoning / [Audio-language model reasoning](https://mlsanity.com/lr/audio-language-model-reasoning/)

## Builds on (most cited first, 22 of 22)

- [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)
- [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)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [ChatMusician: Understanding and Generating Music Intrinsically with LLM](https://mlsanity.com/paper/2402.16153/) (2024)
- [Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles](https://mlsanity.com/paper/2505.19914/) (2025)
- [SynLogic: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond](https://mlsanity.com/paper/2505.19641/) (2025)
- [Foundation Models for Music: A Survey](https://mlsanity.com/paper/2408.14340/) (2024)
- [NotaGen: Advancing Musicality in Symbolic Music Generation with Large Language Model Training Paradigms](https://mlsanity.com/paper/2502.18008/) (2025)
- [Whole-Song Hierarchical Generation of Symbolic Music Using Cascaded Diffusion Models](https://mlsanity.com/paper/2405.09901/) (2024)
- [Sheet Music Transformer: End-To-End Optical Music Recognition Beyond Monophonic Transcription](https://mlsanity.com/paper/2402.07596/) (2024)
- [InternBootcamp: Boosting LLM Reasoning with Verifiable Task Scaling](https://mlsanity.com/paper/2508.08636/) (2025)
- [End-to-End Full-Page Optical Music Recognition for Pianoform Sheet Music](https://mlsanity.com/paper/2405.12105/) (2024)
- [MelodyT5: A Unified Score-to-Score Transformer for Symbolic Music Processing](https://mlsanity.com/paper/2407.02277/) (2024)
- [The Music Maestro or The Musically Challenged, A Massive Music Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2406.15885/) (2024)
- [Aria-MIDI: A Dataset of Piano MIDI Files for Symbolic Music Modeling](https://mlsanity.com/paper/2504.15071/) (2025)
- [Score Transformer: Generating Musical Score from Note-level Representation](https://mlsanity.com/paper/2112.00355/) (2021)
- [Knowledge Discovery in Optical Music Recognition: Enhancing Information Retrieval with Instance Segmentation](https://mlsanity.com/paper/2408.15002/) (2024)
- [MusiXQA: Advancing Visual Music Understanding in Multimodal Large Language Models](https://mlsanity.com/paper/2506.23009/) (2025)

## Built on by (most cited first, 6 of 6)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [LLMZero: Discovering Adaptive Training Strategies for RL Post-Training via LLM Agents](https://mlsanity.com/paper/2606.18388/) (2026)
- [CSyMR: Benchmarking Compositional Music Information Retrieval in Symbolic Music Reasoning](https://mlsanity.com/paper/2601.11556/) (2025)
- [Group Pattern Selection Optimization: Let LRMs Pick the Right Pattern for Reasoning](https://mlsanity.com/paper/2601.07238/) (2026)
- [LEGATO 2: Toward Multimodal Sheet Music Recognition and Understanding](https://mlsanity.com/paper/2607.05769/) (2026)
- [Which Constraints Are Missing? Ask the Verifier: Graded Rewards for Constraint-Following Music Generation](https://mlsanity.com/paper/2609.23665/) (2026)

## Abstract (arXiv)

Enhancing the ability of Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) to interpret sheet music is a crucial step toward building AI musicians. However, current research lacks both evaluation benchmarks and training data for sheet music reasoning. Inspired by mathematics, where simple operations yield infinite verifiable problems, we introduce a novel approach that treats core music theory rules, such as those governing beats and intervals, as programmatic functions to systematically synthesize a vast and diverse corpus of sheet music reasoning problems. This approach allows us to introduce a data synthesis framework that generates verifiable sheet music questions in both textual and visual modalities, leading to the Synthetic Sheet Music Reasoning Benchmark (SSMR-Bench) and a complementary training set. Evaluation results on SSMR-Bench highlight the key role reasoning plays in interpreting sheet music, while also pointing out the ongoing challenges in understanding sheet music in a visual format. By leveraging synthetic data for RLVR, all models show significant improvements on the SSMR-Bench. Additionally, they also demonstrate considerable advancements on previously established human-crafted benchmarks, such as MusicTheoryBench and the music subset of MMMU. Finally, our results show that the enhanced reasoning ability can also facilitate music composition.