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[2601.03612] Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias
Summary
This article presents a novel approach to polyphonic music generation using structural inductive bias, focusing on Beethoven's piano sonatas and demonstrating significant improvements in model efficiency and performance.
Why It Matters
The study addresses the 'Missing Middle' problem in AI music generation, providing a mathematically grounded framework that enhances model stability and generalization. This research is relevant for advancing generative AI applications in music and offers insights for future developments in machine learning.
Key Takeaways
- Introduces a new method for polyphonic music generation.
- Demonstrates a 48.30% reduction in model parameters with Smart Embedding architecture.
- Empirical results show a 9.47% reduction in validation loss.
- Utilizes information theory and category theory for rigorous proofs.
- Bridges theoretical and applied aspects of AI in music generation.
Computer Science > Machine Learning arXiv:2601.03612 (cs) [Submitted on 7 Jan 2026 (v1), last revised 21 Feb 2026 (this version, v3)] Title:Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias Authors:Joonwon Seo View a PDF of the paper titled Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias, by Joonwon Seo View PDF HTML (experimental) Abstract:This monograph introduces a novel approach to polyphonic music generation by addressing the "Missing Middle" problem through structural inductive bias. Focusing on Beethoven's piano sonatas as a case study, we empirically verify the independence of pitch and hand attributes using normalized mutual information (NMI=0.167) and propose the Smart Embedding architecture, achieving a 48.30% reduction in parameters. We provide rigorous mathematical proofs using information theory (negligible loss bounded at 0.153 bits), Rademacher complexity (28.09% tighter generalization bound), and category theory to demonstrate improved stability and generalization. Empirical results show a 9.47% reduction in validation loss, confirmed by SVD analysis and an expert listening study (N=53). This dual theoretical and applied framework bridges gaps in AI music generation, offering verifiable insights for mathematically grounded deep learning. Comments: Subjects: Machine Learning (cs.LG); Sound (cs.SD); Audio and Speech Processing (eess.AS) Cite as: arXiv:2601.03612 [cs.LG] (or arXiv:260...
