Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of practical algorithms. Leveraging mean-field analyses in physics, we propose a novel algorithm for sparse measure recovery. For sparse measures over $\mathbb{R}$, we propose a polynomial-time recovery method from Fourier moments that improves upon convex relaxation methods in a specific parameter regime; then, we demonstrate the application of our results for the optimization of particular two-dimensional, single-layer neural networks in realizable settings.
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In this study, we propose a new index for measuring excellence in science which is based on collaborations (co-authorship distances) in science. The index is based on the Erd\H{o}s number - a number that was introduced several years ago. We propose to focus with the new index on laureates of prestigious prizes in a certain field and to measure co-authorship distances between the laureates and other scientists. To exemplify and explain our proposal, we computed the proposed index in the field of quantitative science studies (PWIPM). The Derek de Solla Price Memorial Award (Price Medal, PM) is awarded to outstanding scientists in the field. We tested the convergent validity of the PWIPM. We were interested whether the indicator is related to an established bibliometric indicator: P(top 10%). The results show that the coefficients for the correlation between PWIPM and P(top 10%) are high (in cases when a sufficient number of papers have been considered for a reliable assessment of performance). Therefore, measured by an established indicator for research excellence, the new PWI indicator seems to be convergently valid and, therefore, might be a possible alternative for established (bibliometric) indicators - with a focus on prizes.
To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.
Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.
Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Visual recognition is currently one of the most important and active research areas in computer vision, pattern recognition, and even the general field of artificial intelligence. It has great fundamental importance and strong industrial needs. Deep neural networks (DNNs) have largely boosted their performances on many concrete tasks, with the help of large amounts of training data and new powerful computation resources. Though recognition accuracy is usually the first concern for new progresses, efficiency is actually rather important and sometimes critical for both academic research and industrial applications. Moreover, insightful views on the opportunities and challenges of efficiency are also highly required for the entire community. While general surveys on the efficiency issue of DNNs have been done from various perspectives, as far as we are aware, scarcely any of them focused on visual recognition systematically, and thus it is unclear which progresses are applicable to it and what else should be concerned. In this paper, we present the review of the recent advances with our suggestions on the new possible directions towards improving the efficiency of DNN-related visual recognition approaches. We investigate not only from the model but also the data point of view (which is not the case in existing surveys), and focus on three most studied data types (images, videos and points). This paper attempts to provide a systematic summary via a comprehensive survey which can serve as a valuable reference and inspire both researchers and practitioners who work on visual recognition problems.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Generative adversarial networks (GANs) are a hot research topic recently. GANs have been widely studied since 2014, and a large number of algorithms have been proposed. However, there is few comprehensive study explaining the connections among different GANs variants, and how they have evolved. In this paper, we attempt to provide a review on various GANs methods from the perspectives of algorithms, theory, and applications. Firstly, the motivations, mathematical representations, and structure of most GANs algorithms are introduced in details. Furthermore, GANs have been combined with other machine learning algorithms for specific applications, such as semi-supervised learning, transfer learning, and reinforcement learning. This paper compares the commonalities and differences of these GANs methods. Secondly, theoretical issues related to GANs are investigated. Thirdly, typical applications of GANs in image processing and computer vision, natural language processing, music, speech and audio, medical field, and data science are illustrated. Finally, the future open research problems for GANs are pointed out.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
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