SiMaN: Sign-to-Magnitude Network Binarization

Binary neural networks (BNNs) have attracted broad research interest due to their efficient storage and computational ability. Nevertheless, a significant challenge of BNNs lies in handling discrete constraints while ensuring bit entropy maximization, which typically makes their weight optimization very difficult. Existing methods relax the learning using the sign function, which simply encodes positive weights into +1s, and -1s otherwise. Alternatively, we formulate an angle alignment objective to constrain the weight binarization to {0,+1} to solve the challenge. In this paper, we show that our weight binarization provides an analytical solution by encoding high-magnitude weights into +1s, and 0s otherwise. Therefore, a high-quality discrete solution is established in a computationally efficient manner without the sign function. We prove that the learned weights of binarized networks roughly follow a Laplacian distribution that does not allow entropy maximization, and further demonstrate that it can be effectively solved by simply removing the $\ell_2$ regularization during network training. Our method, dubbed sign-to-magnitude network binarization (SiMaN), is evaluated on CIFAR-10 and ImageNet, demonstrating its superiority over the sign-based state-of-the-arts. Our source code, experimental settings, training logs and binary models are available at https://github.com/lmbxmu/SiMaN

Sparsity-Inducing Binarized Neural Networks

Binarization of feature representation is critical for Binarized Neural Networks (BNNs). Currently, sign function is the commonly used method for feature binarization. Although it works well on small datasets, the performance on ImageNet remains unsatisfied. Previous methods mainly focus on minimizing quantization error, improving the training strategies and decomposing each convolution layer into several binary convolution modules. However, whether sign is the only option for binarization has been largely overlooked. In this work, we propose the Sparsity-inducing Binarized Neural Network (Si-BNN), to quantize the activations to be either 0 or +1, which introduces sparsity into binary representation. We further introduce trainable thresholds into the backward function of binarization to guide the gradient propagation. Our method dramatically outperforms current state-of-the-arts, lowering the performance gap between full-precision networks and BNNs on mainstream architectures, achieving the new state-of-the-art on binarized AlexNet (Top-1 50.5%), ResNet-18 (Top-1 59.7%), and VGG-Net (Top-1 63.2%). At inference time, Si-BNN still enjoys the high efficiency of exclusive-not-or (xnor) operations