The task of transfer learning using pretrained convolutional neural networks is considered. We propose a convolution-SVD layer to analyze the convolution operators with a singular value decomposition computed in the Fourier domain. Singular vectors extracted from the source domain are transferred to the target domain, whereas the singular values are fine-tuned with a target data set. In this way, dimension reduction is achieved to avoid overfitting, while some flexibility to fine-tune the convolution kernels is maintained. We extend an existing convolution kernel reconstruction algorithm to allow for a reconstruction from an arbitrary set of learned singular values. A generalization bound for a single convolution-SVD layer is devised to show the consistency between training and testing errors. We further introduce a notion of transfer learning gap. We prove that the testing error for a single convolution-SVD layer is bounded in terms of the gap, which motivates us to develop a regularization model with the gap as the regularizer. Numerical experiments are conducted to demonstrate the superiority of the proposed model in solving classification problems and the influence of various parameters. In particular, the regularization is shown to yield a significantly higher prediction accuracy.

考虑使用预训练的卷积神经网络进行迁移学习的任务。我们提出了一个卷积 SVD 层，通过在傅立叶域中计算的奇异值分解来分析卷积算子。从源域提取的奇异向量被转移到目标域，而奇异值则使用目标数据集进行微调。通过这种方式，实现了降维以避免过度拟合，同时保持了微调卷积核的一定灵活性。我们扩展了现有的卷积核重建算法，以允许从任意一组学习的奇异值进行重建。设计了单个卷积 SVD 层的泛化界限，以显示训练和测试误差之间的一致性。我们进一步引入迁移学习差距的概念。我们证明单个卷积 SVD 层的测试误差受间隙限制，这促使我们开发一种以间隙作为正则化器的正则化模型。数值实验证明了该模型在解决分类问题上的优越性以及各种参数的影响。特别是，正则化显示出显着更高的预测精度。