Relationship Between Nonsmoothness in Adversarial Training, Constraints of Attacks, and Flatness in the Input Space.

Adversarial training (AT) is a promising method to improve the robustness against adversarial attacks. However, its performance is not still satisfactory in practice compared with standard training. To reveal the cause of the difficulty of AT, we analyze the smoothness of the loss function in AT, which determines the training performance. We reveal that nonsmoothness is caused by the constraint of adversarial attacks and depends on the type of constraint. Specifically, the L∞ constraint can cause nonsmoothness more than the L2 constraint. In addition, we found an interesting property for AT: the flatter loss surface in the input space tends to have the less smooth adversarial loss surface in the parameter space. To confirm that the nonsmoothness causes the poor performance of AT, we theoretically and experimentally show that smooth adversarial loss by EntropySGD (EnSGD) improves the performance of AT.

A Bayesian Algorithm for Anxiety Index Prediction Based on Cerebral Blood Oxygenation in the Prefrontal Cortex Measured by Near Infrared Spectroscopy.

Stress-induced psychological and somatic diseases are virtually endemic nowadays. Written self-report anxiety measures are available; however, these indices tend to be time consuming to acquire. For medical patients, completing written reports can be burdensome if they are weak, in pain, or in acute anxiety states. Consequently, simple and fast non-invasive methods for assessing stress response from neurophysiological data are essential. In this paper, we report on a study that makes predictions of the state-trait anxiety inventory (STAI) index from oxyhemoglobin and deoxyhemoglobin concentration changes of the prefrontal cortex using a two-channel portable near-infrared spectroscopy device. Predictions are achieved by constructing machine learning algorithms within a Bayesian framework with nonlinear basis function together with Markov Chain Monte Carlo implementation. In this paper, prediction experiments were performed against four different data sets, i.e., two comprising young subjects, and the remaining two comprising elderly subjects. The number of subjects in each data set varied between 17 and 20 and each subject participated only once. They were not asked to perform any task; instead, they were at rest. The root mean square errors for the four groups were 6.20, 6.62, 4.50, and 6.38, respectively. There appeared to be no significant distinctions of prediction accuracies between age groups and since the STAI are defined between 20 and 80, the predictions appeared reasonably accurate. The results indicate potential applications to practical situations such as stress management and medical practice.