Avraam Chatzimichailidis

• Due to its performance, the field of deep learning has gained a lot of attention, with neural networks succeeding in areas like \( \textit{Computer Vision} \) (CV), \( \textit{Neural Language Processing} \) (NLP), and \( \textit{Reinforcement Learning} \) (RL). However, high accuracy comes at a computational cost as larger networks require longer training time and no longer fit onto a single GPU. To reduce training costs, researchers are looking into the dynamics of different optimizers, in order to find ways to make training more efficient. Resource requirements can be limited by reducing model size during training or designing more efficient models that improve accuracy without increasing network size. This thesis combines eigenvalue computation and high-dimensional loss surface visualization to study different optimizers and deep neural network models. Eigenvectors of different eigenvalues are computed, and the loss landscape and optimizer trajectory are projected onto the plane spanned by those eigenvectors. A new parallelization method for the stochastic Lanczos method is introduced, resulting in faster computation and thus enabling high-resolution videos of the trajectory and second-order information during neural network training. Additionally, the thesis presents the loss landscape between two minima along with the eigenvalue density spectrum at intermediate points for the first time. Secondly, this thesis presents a regularization method for \( \textit{Generative Adversarial Networks} \) (GANs) that uses second-order information. The gradient during training is modified by subtracting the eigenvector direction of the biggest eigenvalue, preventing the network from falling into the steepest minima and avoiding mode collapse. The thesis also shows the full eigenvalue density spectra of GANs during training. Thirdly, this thesis introduces ProxSGD, a proximal algorithm for neural network training that guarantees convergence to a stationary point and unifies multiple popular optimizers. Proximal gradients are used to find a closed-form solution to the problem of training neural networks with smooth and non-smooth regularizations, resulting in better sparsity and more efficient optimization. Experiments show that ProxSGD can find sparser networks while reaching the same accuracy as popular optimizers. Lastly, this thesis unifies sparsity and \( \textit{neural architecture search} \) (NAS) through the framework of group sparsity. Group sparsity is achieved through \( \ell_{2,1} \)-regularization during training, allowing for filter and operation pruning to reduce model size with minimal sacrifice in accuracy. By grouping multiple operations together, group sparsity can be used for NAS as well. This approach is shown to be more robust while still achieving competitive accuracies compared to state-of-the-art methods.