Decomposer: Learning to Decompile Symbolic Music to Programs

Abstract: Musical performance involves executing a set of high-level musical instructions, yet recovering those instructions from the performance is a challenging inverse problem. We present Decomposer, a post-training framework for symbolic music decompilation: the task of recovering executable, editable music programs from symbolic music. We instantiate the task as MIDI-to-Strudel decompilation, where the model takes symbolic MIDI as input and produces a program in Strudel, a music programming language, that reconstructs the input when executed. The task poses two challenges: Strudel is a low-resource language with little naturally paired MIDI-code data, and optimizing faithful reconstruction of MIDI alone can collapse to unreadable note-by-note transliteration. We address these challenges in two stages. First, we construct Strudel-Synth, a synthetic corpus of paired Strudel programs and rendered MIDI, and use it for supervised fine-tuning. Second, we refine the model with reinforcement learning on unpaired MIDI, optimizing rewards for both MIDI reconstruction faithfulness and code readability. Our evaluation across synthetic and real-world MIDI benchmarks shows that Decomposer achieves substantially higher MIDI reconstruction faithfulness than closed-source LLMs while producing more readable and diverse code than the heuristic converter.

• The paper introduces a two-stage framework combining supervised fine-tuning and reinforcement learning to generate human-editable Strudel code from MIDI input.
• The methodology leverages a synthetic paired dataset and execution-based rewards to optimize both code readability and output faithfulness.
• Experimental results show significant improvements in compile rates, onset/instrument F1 scores, and code diversity, with robust generalization across musical genres.

Decomposer: Learning to Decompile Symbolic Music to Programs

Problem Definition and Motivation

The inverse problem of translating rendered music into its high-level, human-editable structure is a longstanding challenge central to symbolic music, analogously to established decompilation problems in other artifact domains (e.g., binaries, raster graphics). The paper introduces the task of symbolic music decompilation: recovering editable, executable code in a music programming language (Strudel) from symbolic music input (MIDI). The rationale is grounded in both practicality and usability: rendered MIDI is abundant, but editable code is far more valuable for downstream uses (editing, manipulation, integration with code-based tooling). However, functional output equivalence alone is insufficient—readability and structural abstraction are essential for effective code recovery.

MIDI-to-Strudel decompilation presents unique challenges. There is a lack of large, naturally paired (MIDI, code) data for training. Strudel, a low-resource DSL, exists primarily for algorithmic composition and live coding, representing musical content programmatically through patterns and abstractions, in contrast to event-based MIDI. Existing approaches either yield unreadable, functionally faithful code via direct note-level transliteration (heuristic conversion) or produce readable but poorly grounded programs (frontier LLMs not adapted to the task).

Methodology

Two-Stage Post-Training Framework

The DECOMPOSER framework is designed as a two-stage post-training procedure for open-weight LLMs, specifically targeting MIDI-to-Strudel decompilation:

1. Supervised Fine-Tuning (SFT): A synthetic paired dataset, STRUDEL-SYNTH, is constructed by prompting a frontier LLM (Claude-Opus-4.6) to generate Strudel programs under varied musical and code-style constraints, followed by deterministic cleaning, dead-voice pruning, and headless rendering to obtain the corresponding MIDI. This corpus (21,174 (MIDI, Strudel) pairs) provides sufficient supervision for initial model adaptation.
2. Reinforcement Learning (RL): After SFT, execution-based RL further optimizes the model on unpaired MIDI, leveraging only the MIDI input and Strudel runtime for reward calculation. The composite reward balances MIDI reconstruction faithfulness (instrument-aware onset F1) and code readability (a 12-point LLM-judged rubric). The RL objective is optimized using Group reward-Decoupled normalization Policy Optimization (GDPO), which ensures balanced multi-objective training by per-component normalization before aggregation.

The composite reward is strictly gated on successful code execution. Only executable programs receive non-penalized faithfulness/readability scores, thus driving the model toward practical, correct code.

Data Pipeline

Synthetic data generation relies on prompt-based control of musical attributes (genre, mood, key, tempo, meter, chords, instrumentation) and program idioms (e.g., mini-notation, layered stack, arrange), providing strong coverage of code patterns encountered in Strudel practice. Generated code is systematically cleaned using regex and AST parsing, with non-productive musical voices pruned. The resultant set is considerably more diverse and idiomatic than what web crawl could provide.

Input/Output Representation

MIDI is serialized as instrument-part note events grouped by instrument, with pitches rendered as musical note names and onset times normalized to 'cycle' units matching Strudel's rhythmic abstractions. The model's prompt enforces adherence to Strudel idioms, pattern abstraction, and code style rules relevant for both compilation and human readability.

Experimental Results

Faithfulness–Readability–Diversity Tradeoff

Quantitative evaluations investigate faithfulness (compile rate, onset F1, instrument F1), code readability (LLM-judged rubric, average rank), and code diversity (intra-method CodeBLEU self-similarity) across synthetic (STRUDEL-SYNTH) and real-world (LMD) benchmarks. Baselines include: (a) the heuristic note-level converter (maximal faithfulness, minimal readability), (b) closed-weight frontier LLMs (mid-range readability, low faithfulness), and (c) vanilla Qwen3 models.

Key findings:

• Faithfulness: DECOMPOSER (8B) achieves near-perfect compile rate and the highest Onset/Instrument F1 scores across all settings, substantially outperforming both frontier LLMs (by +0.16–0.32 Onset F1) and open-weight models without adaptation.
• Readability: Code produced by DECOMPOSER scores comparably to frontier LLMs (rubric 0.61–0.74), while the heuristic converter remains an order of magnitude lower (0.05–0.09).
• Diversity: RL-based post-training preserves idiomatic diversity, as measured by SelfCB, avoiding the collapse to fixed templates seen with heuristic methods.

Notably, SFT alone is insufficient for real-world MIDI; execution-based RL yields strong improvements on out-of-domain data without requiring new code annotations.

Ablation and Generalization

Ablation studies clarify the importance of the readability reward and SFT warm start. Increasing the weight of readability improves code quality but can sacrifice faithfulness. Without SFT, RL plateaus at degenerate solutions (verbosity and minimal structure; low reward). Generalization to other datasets (GigaMIDI, NES-MDB, Nottingham, longer LMD) shows robust transfer, with DECOMPOSER maintaining faithfulness and readability advantages over all baselines.

Genre-wise analysis on ModArchive reveals systematic performance gaps: genres with regular rhythmic structure (e.g., electronic, dance) are reconstructed more faithfully than those with irregular timing and dense or expressive textures (e.g., jazz, orchestral, chiptune).

Theoretical and Practical Implications

DECOMPOSER demonstrates that post-training LLMs can acquire the ability to invert the symbolic music process, yielding editable, high-level code from MIDI. This aligns with broader trends in program synthesis, where decompilation is positioned not as a mere transliteration task, but as reconstructing abstract, human-usable structure with verifiable behavioral equivalence.

Implications:

• Editable Music Representations: Converting MIDI to Strudel code enables code-based music editing, facilitating programmatic manipulation, creativity support, and integration with AI-augmented music tooling or live coding contexts.
• Music Structure Reasoning: Mid-level code structures offer improved substrates for both human and model-based music analysis (e.g., motif discovery, music education, abstracted reasoning).
• Expanding Modality Coverage: The reward design (execution-based RL, LLM-judge-based metrics) and synthetic corpus construction are directly extensible to other low-resource code decompilation modalities (e.g., decompiled audio effects, UI reconstruction).

Future Research Directions

The paper identifies several limitations and avenues for further development:

• Reward Conditioning: The fixed readability rubric, while effective, is coarse; future work could use input-conditional, fine-grained evaluation schemes or multi-LLM adjudication.
• Long-Form and Complex Music: Scaling to compositions with significant recurrence and long-range temporal structure will require both larger, more structured datasets and adaptively designed RL rewards.
• Diversity Optimization: Explicitly incorporating output diversity into RL objectives remains unexplored.
• Creative Trace Recovery: Beyond recovering a terminal program, inferring a creative process (progressive code evolution) could offer richer models of musical composition and interaction.

Conclusion

DECOMPOSER advances the state-of-the-art in symbolic music decompilation by integrating synthetic data generation, supervised adaptation, and execution-based RL with multi-objective reward. The resulting system produces Strudel programs from MIDI with superior faithfulness and readability relative to both heuristic and LLM-based baselines, while maintaining output diversity and generalizing across musical domains. This work establishes a methodological and practical precedent for program synthesis with multi-faceted, execution-grounded evaluation in low-resource code domains, with immediate applicability for algorithmic music composition, music education, and AI-augmented creativity tools (2607.01849).