  We study the challenging task of neural network quantization without
end-to-end retraining, called Post-training Quantization (PTQ). PTQ usually
requires a small subset of training data but produces less powerful quantized
models than Quantization-Aware Training (QAT). In this work, we propose a novel
PTQ framework, dubbed BRECQ, which pushes the limits of bitwidth in PTQ down to
INT2 for the first time. BRECQ leverages the basic building blocks in neural
networks and reconstructs them one-by-one. In a comprehensive theoretical study
of the second-order error, we show that BRECQ achieves a good balance between
cross-layer dependency and generalization error. To further employ the power of
quantization, the mixed precision technique is incorporated in our framework by
approximating the inter-layer and intra-layer sensitivity. Extensive
experiments on various handcrafted and searched neural architectures are
conducted for both image classification and object detection tasks. And for the
first time we prove that, without bells and whistles, PTQ can attain 4-bit
ResNet and MobileNetV2 comparable with QAT and enjoy 240 times faster
production of quantized models. Codes are available at
https://github.com/yhhhli/BRECQ.
