A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Discovering multi-purpose modules through deep multitask learning

Machine learning scientists aim to discover techniques that can be applied across diverse sets of problems. Such techniques need to exploit regularities that are shared across tasks. This begs the question: What shared regularity is not yet being exploited? Complex tasks may share structure that is difficult for humans to discover. The goal of deep multitask learning is to discover and exploit this structure automatically by training a joint model across tasks. To this end, this dissertation introduces a deep multitask learning framework for collecting generic functional modules that are used in different ways to solve different problems. Within this framework, a progression of systems is developed based on assembling shared modules into task models and leveraging the complementary advantages of gradient descent and evolutionary optimization. In experiments, these systems confirm that modular sharing improves performance across a range of application areas, including general video game playing, computer vision, natural language processing, and genomics; yielding state-of-the-art results in several cases. The conclusion is that multi-purpose modules discovered by deep multitask learning can exceed those developed by humans in performance and generality.Computer Science

Structured Pruning for Deep Convolutional Neural Networks: A survey

The remarkable performance of deep Convolutional neural networks (CNNs) is generally attributed to their deeper and wider architectures, which can come with significant computational costs. Pruning neural networks has thus gained interest since it effectively lowers storage and computational costs. In contrast to weight pruning, which results in unstructured models, structured pruning provides the benefit of realistic acceleration by producing models that are friendly to hardware implementation. The special requirements of structured pruning have led to the discovery of numerous new challenges and the development of innovative solutions. This article surveys the recent progress towards structured pruning of deep CNNs. We summarize and compare the state-of-the-art structured pruning techniques with respect to filter ranking methods, regularization methods, dynamic execution, neural architecture search, the lottery ticket hypothesis, and the applications of pruning. While discussing structured pruning algorithms, we briefly introduce the unstructured pruning counterpart to emphasize their differences. Furthermore, we provide insights into potential research opportunities in the field of structured pruning. A curated list of neural network pruning papers can be found at https://github.com/he-y/Awesome-Pruning . A dedicated website offering a more interactive comparison of structured pruning methods can be found at: https://huggingface.co/spaces/he-yang/Structured-Pruning-Survey .Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligenc

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition component by integrating the multiresolution framework into the implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition component by integrating the multiresolution framework into the implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm

Modularity in artificial neural networks

Artificial neural networks are deep machine learning models that excel at complex artificial intelligence tasks by abstracting concepts through multiple layers of feature extraction. Modular neural networks are artificial neural networks that are composed of multiple subnetworks called modules. The study of modularity has a long history in the field of artificial neural networks and many of the actively studied models in the domain of artificial neural networks have modular aspects. In this work, we aim to formalize the study of modularity in artificial neural networks and outline how modularity can be used to enhance some neural network performance measures. We do an extensive review of the current practices of modularity in the literature. Based on that, we build a framework that captures the essential properties characterizing the modularization process. Using this modularization framework as an anchor, we investigate the use of modularity to solve three different problems in artificial neural networks: balancing latency and accuracy, reducing model complexity and increasing robustness to noise and adversarial attacks. Artificial neural networks are high-capacity models with high data and computational demands. This represents a serious problem for using these models in environments with limited computational resources. Using a differential architectural search technique, we guide the modularization of a fully-connected network into a modular multi-path network. By evaluating sampled architectures, we can establish a relation between latency and accuracy that can be used to meet a required soft balance between these conflicting measures. A related problem is reducing the complexity of neural network models while minimizing accuracy loss. CapsNet is a neural network architecture that builds on the ideas of convolutional neural networks. However, the original architecture is shallow and has wide layers that contribute significantly to its complexity. By replacing the early wide layers by parallel deep independent paths, we can significantly reduce the complexity of the model. Combining this modular architecture with max-pooling, DropCircuit regularization and a modified variant of the routing algorithm, we can achieve lower model latency with the same or better accuracy compared to the baseline. The last problem we address is the sensitivity of neural network models to random noise and to adversarial attacks, a highly disruptive form of engineered noise. Convolutional layers are the basis of state-of-the-art computer vision models and, much like other neural network layers, they suffer from sensitivity to noise and adversarial attacks. We introduce the weight map layer, a modular layer based on the convolutional layer, that can increase model robustness to noise and adversarial attacks. We conclude our work by a general discussion about the investigated relation between modularity and the addressed problems and potential future research directions

Evolutionary multi-objective optimization in uncertain environments

Ph.DDOCTOR OF PHILOSOPH