28 citations · 43 across the 5 of their papers we have counts for
5 papers
Learning Unstable Dynamical Systems with Time-Weighted Logarithmic Loss
Kamil Nar, Yuan Xue, Andrew M. Dai
When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss functi…
Persistency of Excitation for Robustness of Neural Networks
Kamil Nar, S. Shankar Sastry
When an online learning algorithm is used to estimate the unknown parameters of a model, the signals interacting with the parameter estimates should not decay too quickly for the o…
Cross-Entropy Loss and Low-Rank Features Have Responsibility for Adversarial Examples
Kamil Nar, Orhan Ocal, S. Shankar Sastry +1
State-of-the-art neural networks are vulnerable to adversarial examples; they can easily misclassify inputs that are imperceptibly different than their training and test data. In t…
Step Size Matters in Deep Learning
Kamil Nar, S. Shankar Sastry
Training a neural network with the gradient descent algorithm gives rise to a discrete-time nonlinear dynamical system. Consequently, behaviors that are typically observed in these…
Residual Networks: Lyapunov Stability and Convex Decomposition
Kamil Nar, Shankar Sastry
While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this…