  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.
