Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03612 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911577826918400 |
|---|---|
| author | Seo, Joonwon |
| author_facet | Seo, Joonwon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias Seo, Joonwon Machine Learning Sound Audio and Speech Processing 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. |
| title | Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias |
| topic | Machine Learning Sound Audio and Speech Processing |
| url | https://arxiv.org/abs/2601.03612 |