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This work examines the characteristic activation values of individual ReLUunits in neural networks. We refer to the set of input locations correspondingto such characteristic activation values as the characteristic activation setof a ReLU unit. We draw an explicit connection between the characteristicactivation set and learned features in ReLU networks. This connection leads tonew insights into how various neural network normalization techniques used inmodern deep learning architectures regularize and stabilize stochastic gradientoptimization. Utilizing these insights, we propose geometric parameterizationfor ReLU networks to improve feature learning, which decouples the radial andangular parameters in the hyperspherical coordinate system. We empiricallyverify its usefulness with less carefully chosen initialization schemes andlarger learning rates. We report significant improvements in optimizationstability, convergence speed, and generalization performance for various modelson a variety of datasets, including the ResNet-50 network on ImageNet.

Neural Characteristic Activation Value Analysis for Improved ReLU Network Feature Learning