  Inference for state-of-the-art deep neural networks is computationally
expensive, making them difficult to deploy on constrained hardware
environments. An efficient way to reduce this complexity is to quantize the
weight parameters and/or activations during training by approximating their
distributions with a limited entry codebook. For very low-precisions, such as
binary or ternary networks with 1-8-bit activations, the information loss from
quantization leads to significant accuracy degradation due to large gradient
mismatches between the forward and backward functions. In this paper, we
introduce a quantization method to reduce this loss by learning a symmetric
codebook for particular weight subgroups. These subgroups are determined based
on their locality in the weight matrix, such that the hardware simplicity of
the low-precision representations is preserved. Empirically, we show that
symmetric quantization can substantially improve accuracy for networks with
extremely low-precision weights and activations. We also demonstrate that this
representation imposes minimal or no hardware implications to more
coarse-grained approaches. Source code is available at
https://www.github.com/julianfaraone/SYQ.
