Quantization consists of replacing the original data types used to represent the weights of neural networks with less resource-intensive data types. While considerable research has focused on quantization, most existing methods that offer theoretical guarantees do so by providing error bounds on the difference between the original and reduced precision models.
In this article, we introduce a new quantization technique that, rather than focusing on bounding errors, determines the minimum precision necessary to preserve class dominance, independent of any specific set of numerical formats.
In other words, regardless of the exact scores for each class, our method guarantees that the class predicted by the original network remains unchanged after quantization. Our method is static and the proposed quantization holds for all the inputs.
Technically, we leverage existing theorems that provide error bounds for dot products and formulate an optimization problem whose solution yields the required reduced precision. We also present experimental results to validate the effectiveness of our method.