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Random matrix theory and the loss surfaces of neural networks

arXiv.org Artificial Intelligence

Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of science, engineering and modern life in general. The theoretical understanding of neural networks trails significantly behind their practical success and the engineering heuristics that have grown up around them. Random matrix theory provides a rich framework of tools with which aspects of neural network phenomenology can be explored theoretically. In this thesis, we establish significant extensions of prior work using random matrix theory to understand and describe the loss surfaces of large neural networks, particularly generalising to different architectures. Informed by the historical applications of random matrix theory in physics and elsewhere, we establish the presence of local random matrix universality in real neural networks and then utilise this as a modeling assumption to derive powerful and novel results about the Hessians of neural network loss surfaces and their spectra. In addition to these major contributions, we make use of random matrix models for neural network loss surfaces to shed light on modern neural network training approaches and even to derive a novel and effective variant of a popular optimisation algorithm. Overall, this thesis provides important contributions to cement the place of random matrix theory in the theoretical study of modern neural networks, reveals some of the limits of existing approaches and begins the study of an entirely new role for random matrix theory in the theory of deep learning with important experimental discoveries and novel theoretical results based on local random matrix universality.


Visual Question Answering: A Survey on Techniques and Common Trends in Recent Literature

arXiv.org Artificial Intelligence

Visual Question Answering (VQA) is a multi-disciplinary artificial intelligence research problem that has attracted the attention of researchers from computer vision, natural language processing, knowledge representation, and other machine learning communities. To solve that question, VQA is a task of generating natural language answers when a question in natural language is asked related to an image. In recent years, visual question answering as a result of the flourish in this field, datasets, metrics, and models have been proposed, and the scope of research has been expanded. Although artificial intelligence has solved several different problems, such as image classification and natural language processing (NLP), it is hard to model a problem which needs different types of data. For instance, mixing computer vision with NLP to retrieve some information about an image from a question has tricked researchers for several years.


Convergence of the Inexact Langevin Algorithm and Score-based Generative Models in KL Divergence

arXiv.org Artificial Intelligence

We study the Inexact Langevin Dynamics (ILD), Inexact Langevin Algorithm (ILA), and Score-based Generative Modeling (SGM) when utilizing estimated score functions for sampling. Our focus lies in establishing stable biased convergence guarantees in terms of the Kullback-Leibler (KL) divergence. To achieve these guarantees, we impose two key assumptions: 1) the target distribution satisfies the log-Sobolev inequality (LSI), and 2) the score estimator exhibits a bounded Moment Generating Function (MGF) error. Notably, the MGF error assumption we adopt is more lenient compared to the $L^\infty$ error assumption used in existing literature. However, it is stronger than the $L^2$ error assumption utilized in recent works, which often leads to unstable bounds. We explore the question of how to obtain a provably accurate score estimator that satisfies the MGF error assumption. Specifically, we demonstrate that a simple estimator based on kernel density estimation fulfills the MGF error assumption for sub-Gaussian target distribution, at the population level.


Coordinated Defense Allocation in Reach-Avoid Scenarios with Efficient Online Optimization

arXiv.org Artificial Intelligence

In this paper, we present a dual-layer online optimization strategy for defender robots operating in multiplayer reach-avoid games within general convex environments. Our goal is to intercept as many attacker robots as possible without prior knowledge of their strategies. To balance optimality and efficiency, our approach alternates between coordinating defender coalitions against individual attackers and allocating coalitions to attackers based on predicted single-attack coordination outcomes. We develop an online convex programming technique for single-attack defense coordination, which not only allows adaptability to joint states but also identifies the maximal region of initial joint states that guarantees successful attack interception. Our defense allocation algorithm utilizes a hierarchical iterative method to approximate integer linear programs with a monotonicity constraint, reducing computational burden while ensuring enhanced defense performance over time. Extensive simulations conducted in 2D and 3D environments validate the efficacy of our approach in comparison to state-of-the-art approaches, and show its applicability in wheeled mobile robots and quadcopters.


Milestones in Autonomous Driving and Intelligent Vehicles Part II: Perception and Planning

arXiv.org Artificial Intelligence

Growing interest in autonomous driving (AD) and intelligent vehicles (IVs) is fueled by their promise for enhanced safety, efficiency, and economic benefits. While previous surveys have captured progress in this field, a comprehensive and forward-looking summary is needed. Our work fills this gap through three distinct articles. The first part, a "Survey of Surveys" (SoS), outlines the history, surveys, ethics, and future directions of AD and IV technologies. The second part, "Milestones in Autonomous Driving and Intelligent Vehicles Part I: Control, Computing System Design, Communication, HD Map, Testing, and Human Behaviors" delves into the development of control, computing system, communication, HD map, testing, and human behaviors in IVs. This part, the third part, reviews perception and planning in the context of IVs. Aiming to provide a comprehensive overview of the latest advancements in AD and IVs, this work caters to both newcomers and seasoned researchers. By integrating the SoS and Part I, we offer unique insights and strive to serve as a bridge between past achievements and future possibilities in this dynamic field.


ChatGPT is a Remarkable Tool -- For Experts

arXiv.org Artificial Intelligence

This paper investigates the capabilities of ChatGPT as an automated assistant in diverse domains, including scientific writing, mathematics, education, programming, and healthcare. We explore the potential of ChatGPT to enhance productivity, streamline problem-solving processes, and improve writing style. Furthermore, we highlight the potential risks associated with excessive reliance on ChatGPT in these fields. These limitations encompass factors like incorrect and fictitious responses, inaccuracies in code, limited logical reasoning abilities, overconfidence, and critical ethical concerns of copyrights and privacy violation. We outline areas and objectives where ChatGPT proves beneficial, applications where it should be used judiciously, and scenarios where its reliability may be limited. In light of observed limitations, and given that the tool's fundamental errors may pose a special challenge for non-experts, ChatGPT should be used with a strategic methodology. By drawing from comprehensive experimental studies, we offer methods and flow charts for effectively using ChatGPT. Our recommendations emphasize iterative interaction with ChatGPT and independent verification of its outputs. Considering the importance of utilizing ChatGPT judiciously and with expertise, we recommend its usage for experts who are well-versed in the respective domains.


A Survey on Explainability of Graph Neural Networks

arXiv.org Artificial Intelligence

Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and recommendation systems. However, combining feature information and combinatorial graph structures has led to complex non-linear GNN models. Consequently, this has increased the challenges of understanding the workings of GNNs and the underlying reasons behind their predictions. To address this, numerous explainability methods have been proposed to shed light on the inner mechanism of the GNNs. Explainable GNNs improve their security and enhance trust in their recommendations. This survey aims to provide a comprehensive overview of the existing explainability techniques for GNNs. We create a novel taxonomy and hierarchy to categorize these methods based on their objective and methodology. We also discuss the strengths, limitations, and application scenarios of each category. Furthermore, we highlight the key evaluation metrics and datasets commonly used to assess the explainability of GNNs. This survey aims to assist researchers and practitioners in understanding the existing landscape of explainability methods, identifying gaps, and fostering further advancements in interpretable graph-based machine learning.


Self-supervised Interest Point Detection and Description for Fisheye and Perspective Images

arXiv.org Artificial Intelligence

Keypoint detection and matching is a fundamental task in many computer vision problems, from shape reconstruction, to structure from motion, to AR/VR applications and robotics. It is a well-studied problem with remarkable successes such as SIFT, and more recent deep learning approaches. While great robustness is exhibited by these techniques with respect to noise, illumination variation, and rigid motion transformations, less attention has been placed on image distortion sensitivity. In this work, we focus on the case when this is caused by the geometry of the cameras used for image acquisition, and consider the keypoint detection and matching problem between the hybrid scenario of a fisheye and a projective image. We build on a state-of-the-art approach and derive a self-supervised procedure that enables training an interest point detector and descriptor network. We also collected two new datasets for additional training and testing in this unexplored scenario, and we demonstrate that current approaches are suboptimal because they are designed to work in traditional projective conditions, while the proposed approach turns out to be the most effective.


Prediction of Citrus Diseases Using Machine Learning And Deep Learning: Classifier, Models SLR

arXiv.org Artificial Intelligence

Citrus diseases have been major issues for citrus growing worldwide for many years they can lead significantly reduce fruit quality. the most harmful citrus diseases are citrus canker, citrus greening, citrus black spot, citrus leaf miner which can have significant economic losses of citrus industry in worldwide prevention and management strategies like chemical treatments. Citrus diseases existing in all over the world where citrus is growing its effects the citrus tree root, citrus tree leaf, citrus tree orange etc. Existing of citrus diseases is highly impact on economic factor that can also produce low quality fruits and increased the rate for diseases management. Sanitation and routine monitoring can be effective in managing certain citrus diseases, but others may require more intensive treatments like chemical or biological control methods.


Is Generative Modeling-based Stylization Necessary for Domain Adaptation in Regression Tasks?

arXiv.org Artificial Intelligence

Unsupervised domain adaptation (UDA) aims to bridge the gap between source and target domains in the absence of target domain labels using two main techniques: input-level alignment (such as generative modeling and stylization) and feature-level alignment (which matches the distribution of the feature maps, e.g. gradient reversal layers). Motivated from the success of generative modeling for image classification, stylization-based methods were recently proposed for regression tasks, such as pose estimation. However, use of input-level alignment via generative modeling and stylization incur additional overhead and computational complexity which limit their use in real-world DA tasks. To investigate the role of input-level alignment for DA, we ask the following question: Is generative modeling-based stylization necessary for visual domain adaptation in regression? Surprisingly, we find that input-alignment has little effect on regression tasks as compared to classification. Based on these insights, we develop a non-parametric feature-level domain alignment method -- Implicit Stylization (ImSty) -- which results in consistent improvements over SOTA regression task, without the need for computationally intensive stylization and generative modeling. Our work conducts a critical evaluation of the role of generative modeling and stylization, at a time when these are also gaining popularity for domain generalization.