HyeonSeok Lee

Jinkyu Kim, Hyeonseok Lee, Jinwon Shin

The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential equations as its Euler-Lagrange equation. Thus, it provides elegant structure for the development of versatile temporal finite element methods. Herein, the simplest temporal finite element method is presented by adopting linear temporal shape functions. Numerical examples are included to verify and investigate performance of non-iterative algorithm in the developed method.

Dohun Lim, Hyeonseok Lee, Sungchan Kim

We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points. Our method is built on top of the assumption of smooth landscape in a loss function of the model prediction: locally consistent loss and gradient profile. A theoretical analysis established in this study suggests that those locally smooth model explanations are learned using a batch of noisy copies of the input with the L1 regularization for a saliency map. Extensive experiments support the analysis results, revealing that the proposed saliency maps retrieve the original classes of adversarial examples crafted against both naturally and adversarially trained models, significantly outperforming previous methods. We further demonstrated that such good performance results from the learning capability of this method to identify input features that are truly relevant to the model output of the input and the neighboring data points, fulfilling the requirements of a reliable explanation.

HyeonSeok Lee, Hyo Seon Park

A method to convert real number partitioned activation function into complex number one is provided. The method has 4em variations; 1 has potential to get holomorphic activation, 2 has potential to conserve complex angle, and the last 1 guarantees interaction between real and imaginary parts. The method has been applied to LReLU and SELU as examples. The complex number activation function is an building block of complex number ANN, which has potential to properly deal with complex number problems. But the complex activation is not well established yet. Therefore, we propose a way to extend the partitioned real activation to complex number.