pixels, and can be classified within ten classes. The dataset contains $60,000$ training examples, $10,000$ test examples. Conventional BNNs (non-binarized first layer and no use of stochastic computing), perform very well on this task. With a fully connected BNN with first layer coded with eight bit fixed point real numbers, with two hidden layers of 1024 neurons each and dropout, [ a classification accuracy of $90\%$ can be obtained after 300 epochs]{}. This result is comparable with the test accuracy of $91\%$ obtained by a conventional real-valued neural network with the same architecture.

(topskip=0pt, botskip=0pt, midskip=0pt) \[scale = 0.35\][sto.png]{} [Accuracy on the Fashion MINIST classification task as function of the number of stochastic image presented for the two training methods. Navy blue curve: training of the neural network with grayscale images. Light blue curve: training with presentation of stochastic binarized images. Dashed black line: accuracy when training with a black and white image (i.e. pixels with a value greater than 0.5 are white and pixels that are smaller are black). [ Dashed red line: best accuracy when the binarized neural network is trained on Fashion-MNIST classification task with grayscale images]{}. 300 training epochs were used. \[fig:accuracy\]]{}

Stochastic Computing with Regular 