Analysis of 32-bit Fixed Point Quantizer in the Wide Variance Range for the Laplacian Source

The main goal of this paper is to examine the possibility of using the 32-bit fixed-point format to represent the weights of neural networks (NN) instead of the standardly used 32-bit floating-point format in order to reduce the complexity of NN implementation. To this end, the performance of the 32-bit fixed-point format is analyzed, using an analogy between the fixed-point format and the uniform quantization that allows for the performance of the 32-bit fixed-point format to be expressed by an objective measure SQNR (Signal-to-Quantization Noise Ratio). In doing so, SQNR analysis is performed in a wide range of variance of NN weights, looking for a solution that maximizes the average SQNR in that range of variance. Also, an experiment is performed, applying the 32-bit fixed-point format to represent the weights of an MLP (Multilayer Perceptron) neural network trained for classification purposes. It is shown that the application of the 32-bit fixed-point representation of MLP weights achieves the same classification accuracy as in the case of the 32-bit floating-point representation of MLP weights, proving that the application of the 32-bit fixed-point representation of weights reduces the implementation complexity of neural networks without compromising the accuracy of classification.