提出一种新方法，让深度网络能识别数据中哪些特征重要。
Feature Qualification by Deep Nets: A Constructive Approach
- 利用激活函数为Sigmoid的深层网络构造线性算子
- 该算子可最优逼近光滑径向函数，性能达理论上限
- 能有效判断目标函数的光滑性与径向性，适合特征分析场景
深度学习的成功激发了对深度理论优势的广泛研究，普遍认为深层网络具备逼近和学习多种函数的通用能力。然而这种通用性使难以判断特定任务中哪些数据特征至关重要。本文提出一种构造性方法，通过利用Sigmoid激活函数深层网络的乘积门特性与局部逼近性质，成功构建出一个在逼近光滑径向函数时具有最优逼近性能的线性深层网络算子。进一步地，我们提供了理论证据表明该构造的深层网络算子能够有效识别多个特征，如目标函数的光滑性与径向性。
原文摘要 · Abstract (English)
The great success of deep learning has stimulated avid research activities in verifying the power of depth in theory, a common consensus of which is that deep net are versatile in approximating and learning numerous functions. Such a versatility certainly enhances the understanding of the power of depth, but makes it difficult to judge which data features are crucial in a specific learning task. This paper proposes a constructive approach to equip deep nets for the feature qualification purpose. Using the product-gate nature and localized approximation property of deep nets with sigmoid activation (deep sigmoid nets), we succeed in constructing a linear deep net operator that possesses optimal approximation performance in approximating smooth and radial functions. Furthermore, we provide theoretical evidences that the constructed deep net operator is capable of qualifying multiple features such as the smoothness and radialness of the target functions.
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