Which Constraints Are Missing? Ask the Verifier: Graded Rewards for Constraint-Following Music Generation

arXiv:2609.23665 · cs.SD, cs.AI · Submitted 2026-09-20 · Read on arXiv

cs.SD, cs.AI

Submitted: 2026-09-20

Updated: 2026-09-20

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Verifier — 87× in this paper · explained in 2 episodes
• GRPO — 53× in this paper · explained in 6 episodes
• Benchmark — 22× in this paper · explained in 2 episodes
• Ablation — 10× in this paper · explained in 1 episode
• Calibration — 7× in this paper · explained in 7 episodes
• Reinforcement Learning — 7× in this paper · explained in 4 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Transformer — 5× in this paper · explained in 2 episodes
• Verification — 5× in this paper · explained in 2 episodes
• Fine-Tuning — 3× in this paper · explained in 5 episodes
• Generative AI — 3× in this paper · explained in 2 episodes
• Verifiable Rewards — 3× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Reward Function — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Compositional Generalization — 1× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Provenance — 1× in this paper · explained in 4 episodes

Sources

• MusicLM: Generating Music From Text
• MusicRL: Aligning Music Generation to Human Preferences
• The Llama 3 Herd of Models
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• SymphonyGen: 3D Hierarchical Orchestral Generation with Controllable Harmony Skeleton
• Music Transformer
• Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion
• SMART: Tuning a symbolic music generation system with an audio domain aesthetic reward
• Incorporating Structure and Chord Constraints in Symbolic Transformer-based Melodic Harmonization
• Tulu 3: Pushing Frontiers in Open Language Model Post-Training
• Understanding R1-Zero-Like Training: A Critical Perspective
• Proximal Policy Optimization Algorithms
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Music transcription modelling and composition using deep learning
• Anticipatory Music Transformer
• NotaGen: Advancing Musicality in Symbolic Music Generation with Large Language Model Training Paradigms
• Towards an AI Musician: Synthesizing Sheet Music Problems for Musical Reasoning
• TunesFormer: Forming Irish Tunes with Control Codes by Bar Patching
• Qwen3 Technical Report
• Instruction-Following Evaluation for Large Language Models

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