TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: We propose an approach to training machine learning models that are fair in the sense that their performance is invariant under certain perturbations to the features. For example, the performance of a resume screening system should be invariant under changes to the name of the applicant. We formalize this intuitive notion of fairness by connecting it to the original  notion of individual fairness put forth by Dwork et al and show that the proposed approach achieves this notion of fairness. We also demonstrate the effectiveness of the approach on two machine learning tasks that are susceptible to gender and racial biases.

SOLUTION: Algorithm for training individually fair classifier using adversarial robustness

PROBLEM: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.

SOLUTION: The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.

PROBLEM: The linear transformations in converged deep networks show fast eigenvalue decay. The distribution of eigenvalues looks like a Heavy-tail distribution, where the vast majority of eigenvalues is small, but not actually zero, and only a few spikes of large eigenvalues exist.
 We use a stochastic approximator to generate histograms of eigenvalues. This allows us to investigate layers with hundreds of thousands of dimensions. We show how the distributions change over the course of image net training, converging to a similar heavy-tail spectrum across all intermediate layers.

SOLUTION:
We investigate the eigenvalues of the linear layers in deep networks and show that the distributions develop heavy-tail behavior during training.