Deep neural networks (DNNs) offer the highest performance in a wide range of applications in computer vision. These results rely on over-parameterized backbones, which are expensive to run. This computational burden can be dramatically reduced by quantizing (in either data-free (DFQ), post-training (PTQ) or quantization-aware training (QAT) scenarios) floating point values to ternary values (2 bits, with each weight taking value in {-1,0,1}). In this context, we observe that rounding to nearest minimizes the expected error given a uniform distribution and thus does not account for the skewness and kurtosis of the weight distribution, which strongly affects ternary quantization performance. This raises the following question: shall one minimize the highest or average quantization error? To answer this, we design two operators: TQuant and MQuant that correspond to these respective minimization tasks. We show experimentally that our approach allows to significantly improve the performance of ternary quantization through a variety of scenarios in DFQ, PTQ and QAT and give strong insights to pave the way for future research in deep neural network quantization.
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