研究二次神经微分方程的表达能力，揭示深度如何提升模型性能。
Expressivity of Quadratic Neural ODEs
- 基于迭代复合基础运算实现高表达性
- 深度是决定模型能力的关键因素
- 适用于理解深度学习架构的理论机制
本文研究了动态过程最多包含二次非线性的神经微分方程的定量逼近误差界。该模型结构简单，其表达能力主要源于对基本操作的反复组合，而非单个操作的复杂性。与模拟微分分析器和通用多项式微分代数方程类似，其表达能力主要来自模型的“深度”。这些结果有助于理解深度对深度学习架构能力的具体贡献。
原文摘要 · Abstract (English)
This work focuses on deriving quantitative approximation error bounds for neural ordinary differential equations having at most quadratic nonlinearities in the dynamics. The simple dynamics of this model form demonstrates how expressivity can be derived primarily from iteratively composing many basic elementary operations, versus from the complexity of those elementary operations themselves. Like the analog differential analyzer and universal polynomial DAEs, the expressivity is derived instead primarily from the "depth" of the model. These results contribute to our understanding of what depth specifically imparts to the capabilities of deep learning architectures.
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