AlignQ: Alignment Quantization with ADMM-based Correlation Preservation

Quantization is an efficient network compression approach to reduce the inference time. However, existing approaches ignored the distribution difference between training and testing data, thereby inducing a large quantization error in inference. To address this issue, we propose a new quantization scheme, Alignment Quantization with ADMMbased Correlation Preservation (AlignQ), which exploits the cumulative distribution function (CDF) to align the data to be i.i.d. (independently and identically distributed) for quantization error minimization. Afterward, our theoretical analysis indicates that the significant changes in data correlations after the quantization induce a large quantization error. Accordingly, we aim to preserve the relationship of data from the original space to the aligned quantization space for retaining the prediction information. We design an optimization process by leveraging the Alternating Direction Method of Multipliers (ADMM) optimization to minimize the differences in data correlations before and after the alignment and quantization. In experiments, we visualize non-i.i.d. in training and testing data in the benchmark. We further adopt domain shift data to compare AlignQ with the state-of-the-art. Experimental results show that AlignQ achieves significant performance improvements especially in low-bit models. Code is available at https: //github.com/tinganchen/AlignQ.git . Quantization Large quantization error Training data Testing data Training space Testing space Aligned space for Quantization -0.4 -0.6 +0.8 (c) Data correlations preservation (a) Non-i.i.d data (b) Alignment