SoFAr: Shortcut-based Fractal Architectures for Binary Convolutional Neural Networks

Binary Convolutional Neural Networks (BCNNs) can significantly improve the efficiency of Deep Convolutional Neural Networks (DCNNs) for their deployment on resource-constrained platforms, such as mobile and embedded systems. However, the accuracy degradation of BCNNs is still considerable compared with their full precision counterpart, impeding their practical deployment. Because of the inevitable binarization error in the forward propagation and gradient mismatch problem in the backward propagation, it is nontrivial to train BCNNs to achieve satisfactory accuracy. To ease the difficulty of training, the shortcut-based BCNNs, such as residual connection-based Bi-real ResNet and dense connection-based BinaryDenseNet, introduce additional shortcuts in addition to the shortcuts already present in their full precision counterparts. Furthermore, fractal architectures have been also been used to improve the training process of full-precision DCNNs since the fractal structure triggers effects akin to deep supervision and lateral student-teacher information flow. Inspired by the shortcuts and fractal architectures, we propose two Shortcut-based Fractal Architectures (SoFAr) specifically designed for BCNNs: 1. residual connection-based fractal architectures for binary ResNet, and 2. dense connection-based fractal architectures for binary DenseNet. Our proposed SoFAr combines the adoption of shortcuts and the fractal architectures in one unified model, which is helpful in the training of BCNNs. Results show that our proposed SoFAr achieves better accuracy compared with shortcut-based BCNNs. Specifically, the Top-1 accuracy of our proposed RF-c4d8 ResNet37(41) and DRF-c2d2 DenseNet51(53) on ImageNet outperforms Bi-real ResNet18(64) and BinaryDenseNet51(32) by 3.29% and 1.41%, respectively, with the same computational complexity overhead.