DCFNet: Deep Neural Network with Decomposed Convolutional Filters
DCFNet: Deep Neural Network with Decomposed Convolutional Filters
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发表时间：
2018-02
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通讯作者：
Qiang Qiu;Xiuyuan Cheng;Robert Calderbank;G. Sapiro
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作者：
Qiang Qiu;Xiuyuan Cheng;Robert Calderbank;G. Sapiro
卷积神经网络 (CNN) 中的滤波器包含从大量数据中学习到的模型参数。在本文中，我们建议将 CNN 中的卷积滤波器分解为具有预先固定基数的截断扩展，即分解卷积滤波器网络（DCFNet），其中扩展系数仍然从数据中学习。这种结构不仅减少了可训练参数的数量和计算量，而且还通过碱基截断来强加过滤规则性。通过大量的实验，我们一致观察到 DCFNet 保持了图像分类任务的准确性，同时显着减少了模型参数，特别是在傅里叶贝塞尔 (FB) 基甚至随机基的情况下。理论上，我们分析了 DCFNet 对于输入变化的表示稳定性，并证明了在扩展系数的一般假设下的表示稳定性。分析与经验观察一致。
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of trainable parameters and computation, but also imposes filter regularity by bases truncation. Through extensive experiments, we consistently observe that DCFNet maintains accuracy for image classification tasks with a significant reduction of model parameters, particularly with Fourier-Bessel (FB) bases, and even with random bases. Theoretically, we analyze the representation stability of DCFNet with respect to input variations, and prove representation stability under generic assumptions on the expansion coefficients. The analysis is consistent with the empirical observations.