We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-demand to different bit-widths as energy and memory requirements of the application change. Unlike quantization-aware training using the straight-through estimator that only targets a specific bit-width and requires access to training data and pipeline, our regularization-based method paves the way for "on the fly'' post-training quantization to various bit-widths. We show that by modeling quantization as a $\ell_\infty$-bounded perturbation, the first-order term in the loss expansion can be regularized using the $\ell_1$-norm of gradients. We experimentally validate the effectiveness of our regularization scheme on different architectures on CIFAR-10 and ImageNet datasets.

本文研究了神经网络中权重和激活量化的影响，提出了一种简单的正则化方案来提高其对培训后量化的适应性。通过训练量化-ready的网络，我们的方法可以存储一组可按需量化为不同位宽的权重。我们将量化建模为有界扰动，并使用梯度的L1范数来对其进行正则化，实验证明了我们该方案的有效性。

用于量化鲁棒性的梯度L1正则化