卷积神经网络为何擅长特征提取？一个数学解释
Why do CNNs excel at feature extraction? A mathematical explanation
AI总结：
研究卷积神经网络为何擅长特征提取，引入基于特征提取的新型图像分类数学模型，证明卷积神经网络分类器能零误差解决图像分类任务，构造分段线性函数并表明可由卷积网络实现。
摘要：
在过去十年中，深度学习彻底改变了计算机视觉领域，卷积神经网络模型在图像分类基准测试中非常有效。然而，一个基本的理论问题仍未得到解答：为什么它们能解决涉及特征提取的离散图像分类任务？本文通过引入一种基于特征提取的新型图像分类数学模型来解决这个问题，该模型可用于生成类似于真实世界数据集的图像。我们证明卷积神经网络分类器可以零误差地解决这些图像分类任务。在证明过程中，我们构造了检测特征存在的分段线性函数，并表明它们可以由卷积网络实现。
英文摘要：
Over the past decade deep learning has revolutionized the field of computer vision, with convolutional neural network models proving to be very effective for image classification benchmarks. However, a fundamental theoretical questions remain answered: why can they solve discrete image classification tasks that involve feature extraction? We address this question in this paper by introducing a novel mathematical model for image classification, based on feature extraction, that can be used to generate images resembling real-world datasets. We show that convolutional neural network classifiers can solve these image classification tasks with zero error. In our proof, we construct piecewise linear functions that detect the presence of features, and show that they can be realized by a convolutional network.
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