in an ASIC, the non binarized neural network requires energy-hungry 8-bits multiplications and addition ($0.3~pJ$ and $0.04~pJ$ per operation in our $28~nm$ technology). Taking into account only these arithmetic operations, the energy consumption is $220~nJ$ for recognizing a Fashion-MNIST image with the same accuracy as the stochastic BNN with three image presentations. This stochastic BNN requires only $90~nJ$ (Fig. \[fig:energy\]), taking into account the whole system. ]{}

[ As a conclusion, this works highlights that the stochastic computing approach is attractive in terms of area occupancy.]{} In terms of energy efficiency, it is very attractive if a relatively small number of presentation is used ($T<8$). Therefore, it appears preferable to rely on the stochastic training approach seen in section \[sec:adaptedtrainig\], and to use few stochastic image presentation for inference. For example, if three image presentation are used, a factor $2.1$ can be saved on the energy consumption on Fashion-MNIST, with a reduction of [$1.4\%$]{} of test accuracy with regards to the best accuracy obtained by a BNN (dashed red line in Fig. \[fig:accuracy\]). It should be noticed that the benefits of stochastic computing would be reduced on very deep neural networks, where the first layer plays a smaller role. Our 