用数学方法让音乐生成更连贯，减少48%参数量
Mathematical Foundations of Polyphonic Music Generation via Structural Inductive Bias
- 将音高与手部动作解耦建模，基于实证独立性设计结构化嵌入
- 参数量减少48.3%，验证损失降低9.47%，泛化能力提升28.09%
- 适合关注音乐生成可解释性与高效建模的研究者
本文针对人工智能音乐生成中的‘缺失中间层’问题——即难以生成连贯的乐句结构——以贝多芬钢琴奏鸣曲为案例，提出智能嵌入（Smart Embedding）架构。该架构基于音高与手部属性在经验上独立的发现（NMI=0.167），采用因子化表示，在保持性能的同时使嵌入参数减少48.3%，并使验证损失下降9.47%。理论上，通过信息论、Rademacher复杂度分析（泛化界收紧28.09%）及范畴论解释建立形式化保证。支持性证据包括奇异值分解分析和盲听专家评测（N=53）。本工作融合架构创新与数学严谨性，为复杂序列数据生成提供可解释、高效且稳定的原理框架。
原文摘要 · Abstract (English)
This monograph addresses the "Missing Middle" problem in AI music generation - the challenge of producing coherent, phrase-level musical structure. Using Beethoven's piano sonatas as a case study, I introduce the Smart Embedding architecture, a factorized representation grounded in the empirically verified independence of pitch and hand attributes (NMI=0.167). The architecture achieves a 48.3% reduction in embedding parameters while improving validation loss by 9.47%. Theoretically, I establish formal guarantees through information theory, Rademacher complexity analysis (yielding a 28.09% tighter generalization bound), and category-theoretic interpretation. These results are further supported by Singular Value Decomposition analysis and a blind expert listening study (N=53). Collectively, this work presents a dual contribution that combines architectural innovation with mathematical rigor, offering a principled framework for building more efficient, stable, and interpretable generative models for complex sequential data.
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