分析散射网络的分类能力，揭示其特征提取性能的关键因素。
Separation Capacity of Scattering Networks
- 基于覆盖理论构建分离容量的新公式，更直观且实用。
- 发现散射网络的分离容量由其网络组件共同决定。
- 为散射网络设计提供可操作的优化方向，适合模型研究者。
本文尝试通过覆盖函数计数理论深化对卷积神经网络（CNN）作为分类任务特征提取器的理论理解。核心关注点是分离容量——一种从可实现二分划分数量推导出的组合量。贡献有三：首先，扩展覆盖框架，提出概念清晰且实用的分离容量新表述；其次，基于该表述，识别出特定架构的散射网络中影响分离容量的关键因素，与网络构建模块相关；最后，为散射网络的设计提供实用指导。
原文摘要 · Abstract (English)
In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separation capacity, a combinatorial quantity derived from counting the number of realizable dichotomies (i.e., binary label assignments). Our contributions are threefold. First, we extend Cover's framework by establishing a conceptually insightful and practically useful formulation for the separation capacity. Second, leveraging this formulation, we identify the factors governing the separation capacity of feature extractors that employ a specific CNN architecture, so-called scattering networks, in terms of their network building blocks. Third, we provide practical insights for scattering network design.
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