The effects of quantization on high order function neural networks

This paper paid attention to the combined effects of quantization and clipping on performance of high order function neural networks (HOFNN) for simpler and more reliable hardware implementation. We probed into how to make the effects of quantization as small as possible to ensure certain training and non-linear ability at a given standard. We established in theory and proved the relationships among bit resolution of inputs and outputs, training and quantization manners, network-order number and performance degradation in HOFNN, showing that (1) signal to noise ratio (SNR) decrease followed with the increasing number of orders in a fixed bits; (2) SNR increase followed with the increasing number of bits; (3) the amplifying factor of SNR through nonlinear neuron, which is always less than 1, is unrelated with quantization error. The experiments revealed that the number of orders in HOFNN is more sensitiv for performance in the low bits of quantization and the simulate results conform with our proposed theoretical analysis.