FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes

When designing Convolutional Neural Networks (CNNs), one must select the size of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice... A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which high bandwidth convolutional kernels of learnable kernel size can be learned at a fixed parameter cost. FlexNets model long-term dependencies without the use of pooling, achieve state-of-the-art performance on several sequential datasets, outperform recent works with learned kernel sizes, and are competitive with much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be deployed at higher resolutions than those seen during training. To avoid aliasing, we propose a novel kernel parameterization with which the frequency of the kernels can be analytically controlled. Our novel kernel parameterization shows higher descriptive power and faster convergence speed than existing parameterizations. This leads to important improvements in classification accuracy. read more

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Image Classification CIFAR-10 FlexTCN-7 Percentage correct 92.2±0.1 # 138
PARAMS 0.67M # 141
Sequential Image Classification noise padded CIFAR-10 FlexTCN-6 % Test Accuracy 69.87% # 1
Sequential Image Classification Sequential CIFAR-10 FlexTCN-6 Unpermuted Accuracy 80.82% # 2
Sequential Image Classification Sequential MNIST FlexTCN-6 Unpermuted Accuracy 99.62% # 2
Sequential Image Classification Sequential MNIST FlexTCN-4 Permuted Accuracy 98.72% # 1
Time Series Speech Commands FlexTCN-4 % Test Accuracy 97.73 # 1
Time Series Speech Commands FlexTCN-6 % Test Accuracy (Raw Data) 91.73 # 1


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