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We revisit fuzzy neural network with a cornerstone notion of generalizedhamming distance, which provides a novel and theoretically justified frameworkto re-interpret many useful neural network techniques in terms of fuzzy logic.In particular, we conjecture and empirically illustrate that, the celebratedbatch normalization (BN) technique actually adapts the normalized bias suchthat it approximates the rightful bias induced by the generalized hammingdistance. Once the due bias is enforced analytically, neither the optimizationof bias terms nor the sophisticated batch normalization is needed. Also in thelight of generalized hamming distance, the popular rectified linear units(ReLU) can be treated as setting a minimal hamming distance threshold betweennetwork inputs and weights. This thresholding scheme, on the one hand, can beimproved by introducing double thresholding on both extremes of neuron outputs.On the other hand, ReLUs turn out to be non-essential and can be removed fromnetworks trained for simple tasks like MNIST classification. The proposedgeneralized hamming network (GHN) as such not only lends itself to rigorousanalysis and interpretation within the fuzzy logic theory but also demonstratesfast learning speed, well-controlled behaviour and state-of-the-artperformances on a variety of learning tasks.

Revisit Fuzzy Neural Network: Demystifying Batch Normalization and ReLU with Generalized Hamming Network