Many deep neural networks are built by using stacked convolutional layers of fixed and single size (often 3$\times$3) kernels. This paper describes a method for training the size of convolutional kernels to provide varying size kernels in a single layer. The method utilizes a differentiable, and therefore backpropagation-trainable Gaussian envelope which can grow or shrink in a base grid. Our experiments compared the proposed adaptive layers to ordinary convolution layers in a simple two-layer network, a deeper residual network, and a U-Net architecture. The results in the popular image classification datasets such as MNIST, MNIST-CLUTTERED, CIFAR-10, Fashion, and ``Faces in the Wild'' showed that the adaptive kernels can provide statistically significant improvements on ordinary convolution kernels. A segmentation experiment in the Oxford-Pets dataset demonstrated that replacing a single ordinary convolution layer in a U-shaped network with a single 7$\times$7 adaptive layer can improve its learning performance and ability to generalize.

中文翻译：

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人工神经网络的自适应卷积核

许多深度神经网络是通过使用固定和单一大小（通常为 3$\times$3）内核的堆叠卷积层构建的。本文描述了一种训练卷积核大小的方法，以在单层中提供不同大小的内核。该方法利用可微分，因此可以反向传播训练的高斯包络，它可以在基础网格中增长或缩小。我们的实验将所提出的自适应层与简单的两层网络、更深的残差网络和 U-Net 架构中的普通卷积层进行了比较。在 MNIST、MNIST-CLUTTERED、CIFAR-10、Fashion 和“Faces in the Wild”等流行图像分类数据集上的结果表明，自适应内核可以对普通卷积内核提供统计上显着的改进。