Learning Sparse & Ternary Neural Networks with Entropy-Constrained Trained Ternarization (EC2T)

Deep neural networks (DNN) have shown remarkable success in a variety of machine learning applications. The capacity of these models (i.e., number of parameters), endows them with expressive power and allows them to reach the desired performance. In recent years, there is an increasing interest in deploying DNNs to resource-constrained devices (i.e., mobile devices) with limited energy, memory, and computational budget. To address this problem, we propose Entropy-Constrained Trained Ternarization (EC2T), a general framework to create sparse and ternary neural networks which are efficient in terms of storage (e.g., at most two binary-masks and two full-precision values are required to save a weight matrix) and computation (e.g., MAC operations are reduced to a few accumulations plus two multiplications). This approach consists of two steps. First, a super-network is created by scaling the dimensions of a pre-trained model (i.e., its width and depth). Subsequently, this super-network is simultaneously pruned (using an entropy constraint) and quantized (that is, ternary values are assigned layer-wise) in a training process, resulting in a sparse and ternary network representation. We validate the proposed approach in CIFAR-10, CIFAR-100, and ImageNet datasets, showing its effectiveness in image classification tasks.Comment: Proceedings of the CVPR'20 Joint Workshop on Efficient Deep Learning in Computer Vision. Code is available at https://github.com/d-becking/efficientCNN

Forward and Backward Information Retention for Accurate Binary Neural Networks

Weight and activation binarization is an effective approach to deep neural network compression and can accelerate the inference by leveraging bitwise operations. Although many binarization methods have improved the accuracy of the model by minimizing the quantization error in forward propagation, there remains a noticeable performance gap between the binarized model and the full-precision one. Our empirical study indicates that the quantization brings information loss in both forward and backward propagation, which is the bottleneck of training accurate binary neural networks. To address these issues, we propose an Information Retention Network (IR-Net) to retain the information that consists in the forward activations and backward gradients. IR-Net mainly relies on two technical contributions: (1) Libra Parameter Binarization (Libra-PB): simultaneously minimizing both quantization error and information loss of parameters by balanced and standardized weights in forward propagation; (2) Error Decay Estimator (EDE): minimizing the information loss of gradients by gradually approximating the sign function in backward propagation, jointly considering the updating ability and accurate gradients. We are the first to investigate both forward and backward processes of binary networks from the unified information perspective, which provides new insight into the mechanism of network binarization. Comprehensive experiments with various network structures on CIFAR-10 and ImageNet datasets manifest that the proposed IR-Net can consistently outperform state-of-the-art quantization methods