  Quantization based on the binary codes is gaining attention because each
quantized bit can be directly utilized for computations without dequantization
using look-up tables. Previous attempts, however, only allow for integer
numbers of quantization bits, which ends up restricting the search space for
compression ratio and accuracy. In this paper, we propose an encryption
algorithm/architecture to compress quantized weights so as to achieve
fractional numbers of bits per weight. Decryption during inference is
implemented by digital XOR-gate networks added into the neural network model
while XOR gates are described by utilizing $\tanh(x)$ for backward propagation
to enable gradient calculations. We perform experiments using MNIST, CIFAR-10,
and ImageNet to show that inserting XOR gates learns quantization/encrypted bit
decisions through training and obtains high accuracy even for fractional sub
1-bit weights. As a result, our proposed method yields smaller size and higher
model accuracy compared to binary neural networks.
