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Lately, post-training quantization methods have gained considerableattention, as they are simple to use, and require only a small unlabeledcalibration set. This small dataset cannot be used to fine-tune the modelwithout significant over-fitting. Instead, these methods only use thecalibration set to set the activations' dynamic ranges. However, such methodsalways resulted in significant accuracy degradation, when used below 8-bits(except on small datasets). Here we aim to break the 8-bit barrier. To thisend, we minimize the quantization errors of each layer separately by optimizingits parameters over the calibration set. We empirically demonstrate that thisapproach is: (1) much less susceptible to over-fitting than the standardfine-tuning approaches, and can be used even on a very small calibration set;and (2) more powerful than previous methods, which only set the activations'dynamic ranges. Furthermore, we demonstrate how to optimally allocate thebit-widths for each layer, while constraining accuracy degradation or modelcompression by proposing a novel integer programming formulation. Finally, wesuggest model global statistics tuning, to correct biases introduced duringquantization. Together, these methods yield state-of-the-art results for bothvision and text models. For instance, on ResNet50, we obtain less than 1\%accuracy degradation --- with 4-bit weights and activations in all layers, butthe smallest two. We open-sourced our code.

Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming