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.

翻译：本专著通过结构归纳偏置解决"缺失中间层"问题，提出了一种新颖的复调音乐生成方法。以贝多芬钢琴奏鸣曲为案例研究，我们利用归一化互信息（NMI=0.167）实证验证了音高与手部属性的独立性，并提出了Smart Embedding架构，实现了参数数量减少48.30%。我们运用信息论（可忽略损失上界为0.153比特）、Rademacher复杂度（泛化界收紧28.09%）和范畴论提供了严格的数学证明，以论证模型稳定性与泛化能力的提升。实证结果表明验证损失降低9.47%，该结果通过奇异值分解分析和专家听辨实验（N=53）得以验证。这一理论与应用相结合的双重框架弥合了人工智能音乐生成领域的空白，为基于数学的深度学习提供了可验证的见解。