data of MNIST was used to train the network and the test data of MNIST was used as validation data.

In MNIST, the image size is $28\times28$, thus there are 784 pixels, which are used as input neurons. As mentioned above, in order to make the neurons of the input layer an odd number, one neuron was simply added to the input layer and set to $1$. Consequently, the input layer contains 785 neurons. Moreover, since the digits have 10 classes, so the output layer is set to 10 neurons.

For the hidden layer, we used two different numbers, one is 1571 (double of the input neuron number) and the other is 2355 (three times of the input neuron number). Then, two different network structures are obtained as follows.

-   Structure A: the input layer contains 785 neurons, followed by a hidden layer of 1571 neurons, then an output layer of 10 neurons (one neuron stands for one digit class).

-   Structure B: the input layer contains 785 neurons, followed by a hidden layer of 2355 neurons, then an output layer of 10 neurons (one neuron stands for one digit class).

In the experiments, the BDNN of both structures were 