CSQ: Centered Symmetric Quantization for Extremely Low Bit Neural Networks

Recent advances in quantized neural networks (QNNs) are closing the performance gap with the full precision neural networks. However at very low precision (i.e., $\le 3$-bits), QNNs often still suffer significant performance degradation. The conventional uniform symmetric quantization scheme allocates unequal numbers of positive and negative quantization levels. We show that this asymmetry in the number of positive and negative quantization levels can result in significant quantization error and performance degradation at low precision. We propose and analyze a quantizer called centered symmetric quantizer (CSQ), which preserves the symmetry of latent distribution by providing equal representations to the negative and positive sides of the distribution. We also propose a novel method to efficiently map CSQ to binarized neural network hardware using bitwise operations. Our analyses and experimental results using state-of-the-art quantization methods on ImageNet and CIFAR-10 show the importance of using CSQ for weight in place of the conventional quantization scheme at extremely low-bit precision (2$\sim$3 bits).