First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their widespread, second-order optimization algorithms exhibit superior convergence properties compared to their first-order counterparts e.g. Adam and SGD. However, their practicality in training DNNs are still limited due to increased per-iteration computations and suboptimal accuracy compared to the first order methods. We present AdaFisher--an adaptive second-order optimizer that leverages a block-diagonal approximation to the Fisher information matrix for adaptive gradient preconditioning. AdaFisher aims to bridge the gap between enhanced convergence capabilities and computational efficiency in second-order optimization framework for training DNNs. Despite the slow pace of second-order optimizers, we showcase that AdaFisher can be reliably adopted for image classification, language modelling and stand out for its stability and robustness in hyperparameter tuning. We demonstrate that AdaFisher outperforms the SOTA optimizers in terms of both accuracy and convergence speed. Code available from \href{https://github.com/AtlasAnalyticsLab/AdaFisher}{https://github.com/AtlasAnalyticsLab/AdaFisher}

Differentiable Architecture Search (DARTS) has attracted considerable attention as a gradient-based neural architecture search method. Since the introduction of DARTS, there has been little work done on adapting the action space based on state-of-art architecture design principles for CNNs. In this work, we aim to address this gap by incrementally augmenting the DARTS search space with micro-design changes inspired by ConvNeXt and studying the trade-off between accuracy, evaluation layer count, and computational cost. We introduce the Pseudo-Inverted Bottleneck Conv (PIBConv) block intending to reduce the computational footprint of the inverted bottleneck block proposed in ConvNeXt. Our proposed architecture is much less sensitive to evaluation layer count and outperforms a DARTS network with similar size significantly, at layer counts as small as 2. Furthermore, with less layers, not only does it achieve higher accuracy with lower computational footprint (measured in GMACs) and parameter count, GradCAM comparisons show that our network can better detect distinctive features of target objects compared to DARTS. Code is available from https://github.com/mahdihosseini/PIBConv.

The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO method and explore how the low-rank factorization of the convolutional weights of intermediate layers of a convolutional neural network can be used to define an analytical response surface for optimizing hyper-parameters, using only training data. We quantify how this surface behaves as a surrogate to model performance and can be solved using a trust-region search algorithm, which we call autoHyper. The algorithm outperforms state-of-the-art such as Bayesian Optimization and generalizes across model, optimizer, and dataset selection. Our code can be found at \url{https://github.com/MathieuTuli/autoHyper}.

Neural Architecture Search (NAS) has been pivotal in finding optimal network configurations for Convolution Neural Networks (CNNs). While many methods explore NAS from a global search-space perspective, the employed optimization schemes typically require heavy computational resources. This work introduces a method that is efficient in computationally constrained environments by examining the micro-search space of channel size. In tackling channel-size optimization, we design an automated algorithm to extract the dependencies within different connected layers of the network. In addition, we introduce the idea of knowledge distillation, which enables preservation of trained weights, admist trials where the channel sizes are changing. Further, since the standard performance indicators (accuracy, loss) fail to capture the performance of individual network components (providing an overall network evaluation), we introduce a novel metric that highly correlates with test accuracy and enables analysis of individual network layers. Combining dependency extraction, metrics, and knowledge distillation, we introduce an efficient searching algorithm, with simulated annealing inspired stochasticity, and demonstrate its effectiveness in finding optimal architectures that outperform baselines by a large margin.

The choice of step-size used in Stochastic Gradient Descent (SGD) optimization is empirically selected in most training procedures. Moreover, the use of scheduled learning techniques such as Step-Decaying, Cyclical-Learning, and Warmup to tune the step-size requires extensive practical experience--offering limited insight into how the parameters update--and is not consistent across applications. This work attempts to answer a question of interest to both researchers and practitioners, namely \textit{"how much knowledge is gained in iterative training of deep neural networks?"} Answering this question introduces two useful metrics derived from the singular values of the low-rank factorization of convolution layers in deep neural networks. We introduce the notions of \textit{"knowledge gain"} and \textit{"mapping condition"} and propose a new algorithm called Adaptive Scheduling (AdaS) that utilizes these derived metrics to adapt the SGD learning rate proportionally to the rate of change in knowledge gain over successive iterations. Experimentation reveals that, using the derived metrics, AdaS exhibits: (a) faster convergence and superior generalization over existing adaptive learning methods; and (b) lack of dependence on a validation set to determine when to stop training. Code is available at \url{https://github.com/mahdihosseini/AdaS}.