Proposition 2. F or a given group a A, gradient norms can be upper bounded as: g Proposition 3. Consider a binary classifier B.1 Datasets The paper uses the following datasets to validate the findings discussed in the main paper: The experiments adopt the following attributes for classification (e.g., Y) and as protected group ( A): ethnicity, age bins, gender. B.2 Architectures, Hyper-parameters, and Settings The study adopts the following architectures to validate the results of the main paper: The model has 11 million trainable parameters. ResNet50 This model contains 48 convolution layers, 1 MaxPool layer and a AvgPool layer. ResNet50 has 25 million trainable parameters. VGG-19 This model consists of 19 layers (16 convolution layers, 3 fully connected layers, 5 MaxPool layers and 1 SoftMax layer).

Network pruning is a widely-used compression technique that is able to significantly scale down overparameterized models with minimal loss of accuracy. This paper shows that pruning may create or exacerbate disparate impacts. The paper sheds light on the factors to cause such disparities, suggesting differences in gradient norms and distance to decision boundary across groups to be responsible for this critical issue. It analyzes these factors in detail, providing both theoretical and empirical support, and proposes a simple, yet effective, solution that mitigates the disparate impacts caused by pruning.