Resiliency of Deep Neural Networks under Quantization

The complexity of deep neural network algorithms for hardware implementation can be much lowered by optimizing the word-length of weights and signals. Direct quantization of floating-point weights, however, does not show good performance when the number of bits assigned is small. Retraining of quantized networks has been developed to relieve this problem. In this work, the effects of quantization are analyzed for a feedforward deep neural network (FFDNN) and a convolutional neural network (CNN) when their network complexity is changed. The complexity of the FFDNN is controlled by varying the unit size in each hidden layer and the number of layers, while that of the CNN is done by modifying the feature map configuration. We find that some performance gap exists between the floatingpoint and the retrain-based ternary (+1, 0, -1) weight neural networks when the size is not large enough, but the discrepancy almost vanishes in fully complex networks whose capability is limited by the training data, rather than by the number of connections. This research shows that highly complex DNNs have the capability of absorbing the effects of severe weight quantization through retraining, but connection limited networks are less resilient. This paper also presents the effective compression ratio to guide the trade-off between the network size and the precision when the hardware resource is limited.