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Gradient \(\ell_1\) Regularization for Quantization Robustness

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 our method on different architectures on CIFAR-10 and ImageNet datasets and show that the regularization of a neural network using our method improves robustness against quantization noise.

Milad Alizadeh, Arash Behboodi, Mart van Baalen, Christos Louizos, Tijmen Blankevoort, Max Welling
ICLR, 2020

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