Abstract
   We propose an optimization algorithm that uses second-derivative information, exploiting curvature information for avoiding saddle points. We utilize a Hessian-free approach where we do not explicitly store the second-derivative matrix, by applying a conjugate gradient method. Secondly, we propose using a limited-memory symmetric rank-one quasi-Newton approach which further addresses the time and space computational complexity. The approach allows for indefinite Hessian approximations, enabling directions of negative curvature to be exploited. Furthermore, we use a modified adaptive regularized using cubics approach, which generates a sequence of cubic subproblems with closed-form solutions. Secondly, we propose a quasi-Adam approach. Judicious choices of quasi-Newton matrices can lead to guaranteed descent in the objective function and improved convergence. Finally, we propose a variety of architectures for various applications - 1. A blind source signal separator, which involves separating image signals which have been superimposed by a common observing apparatus, 2. A novel deep learning architectures for low photon count image denoising, which contains Gaussian noise in a low-photon count setting, 3. A novel architecture for lowphoton count and downsampled imaging, where the signal is interfered with mixed Gaussian and Poisson noise and then downsampled, 4. A novel adversarial detection method for white-box attacks using Radial basis function and Discrete Cosine Transforms.

Biography
   Aditya Ranganath is a PhD candidate in the Electrical Engineering and Computer Science department at the University of California, Merced. He is currently advised by Dr. Mukesh and Dr. Roummel Marcia. His research interests include Optimization techniques for machine learning and deep learning and image processing techniques. He received his Bachelor’s in Electrical Engineering from Loyola-ICAM College of Engineering and Technology in Chenna, India.