The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the underlying data and task. Moreover, conventional distance functions limit the space of similarity measures to be symmetric and do not directly allow comparing objects from different spaces. We propose using quantum networks (GQSim) for learning task-dependent (a)symmetric similarity between data that need not have the same dimensionality. We analyze the properties of such similarity function analytically (for a simple case) and numerically (for a complex case) and showthat these similarity measures can extract salient features of the data. We also demonstrate that the similarity measure derived using this technique is $(\epsilon,\gamma,\tau)$-good, resulting in theoretically guaranteed performance. Finally, we conclude by applying this technique for three relevant applications - Classification, Graph Completion, Generative modeling.
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Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being dedicated by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the QCN performance. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite quantum states' lifetime. In this paper, we introduce a novel framework, dubbed physics-informed QCNs, for designing and analyzing the performance of QCNs, by relying on the quantum physics principles that underly the different QCN components. The need of the proposed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-the-art advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of future communication networks (6G and beyond, and the quantum Internet).
Crime has become a major concern in many cities, which calls for the rising demand for timely predicting citywide crime occurrence. Accurate crime prediction results are vital for the beforehand decision-making of government to alleviate the increasing concern about the public safety. While many efforts have been devoted to proposing various spatial-temporal forecasting techniques to explore dependence across locations and time periods, most of them follow a supervised learning manner, which limits their spatial-temporal representation ability on sparse crime data. Inspired by the recent success in self-supervised learning, this work proposes a Spatial-Temporal Hypergraph Self-Supervised Learning framework (ST-HSL) to tackle the label scarcity issue in crime prediction. Specifically, we propose the cross-region hypergraph structure learning to encode region-wise crime dependency under the entire urban space. Furthermore, we design the dual-stage self-supervised learning paradigm, to not only jointly capture local- and global-level spatial-temporal crime patterns, but also supplement the sparse crime representation by augmenting region self-discrimination. We perform extensive experiments on two real-life crime datasets. Evaluation results show that our ST-HSL significantly outperforms state-of-the-art baselines. Further analysis provides insights into the superiority of our ST-HSL method in the representation of spatial-temporal crime patterns. The implementation code is available at //github.com/LZH-YS1998/STHSL.
Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules or applying parameters to small molecules or biopolymers, making it difficult to optimize both types and parameters to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph neural networks to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using invariance-preserving layers. Since all stages are built from smooth neural functions, the entire process is modular and end-to-end differentiable with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach is not only sufficiently expressive to reproduce legacy atom types, but that it can learn to accurately reproduce and extend existing molecular mechanics force fields. Trained with arbitrary loss functions, it can construct entirely new force fields self-consistently applicable to both biopolymers and small molecules directly from quantum chemical calculations, with superior fidelity than traditional atom or parameter typing schemes. When trained on the same quantum chemical small molecule dataset used to parameterize the openff-1.2.0 small molecule force field augmented with a peptide dataset, the resulting espaloma model shows superior accuracy vis-\`a-vis experiments in computing relative alchemical free energy calculations for a popular benchmark set.
In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its $\ell_1/\ell_2$-estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and source are sufficiently close to each other, these bounds could be improved over those of the classical penalized estimator using only target data under mild conditions. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. We also propose an algorithm to construct confidence intervals of each coefficient component, and the corresponding theories are provided. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms. We implement the proposed GLM transfer learning algorithms in a new R package glmtrans, which is available on CRAN.
Ambient lighting conditions play a crucial role in determining the perceptual quality of images from photographic devices. In general, inadequate transmission light and undesired atmospheric conditions jointly degrade the image quality. If we know the desired ambient factors associated with the given low-light image, we can recover the enhanced image easily \cite{b1}. Typical deep networks perform enhancement mappings without investigating the light distribution and color formulation properties. This leads to a lack of image instance-adaptive performance in practice. On the other hand, physical model-driven schemes suffer from the need for inherent decompositions and multiple objective minimizations. Moreover, the above approaches are rarely data efficient or free of postprediction tuning. Influenced by the above issues, this study presents a semisupervised training method using no-reference image quality metrics for low-light image restoration. We incorporate the classical haze distribution model \cite{b2} to explore the physical properties of the given image in order to learn the effect of atmospheric components and minimize a single objective for restoration. We validate the performance of our network for six widely used low-light datasets. The experiments show that the proposed study achieves state-of-the-art or comparable performance.
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.
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.
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.
Deep neural networks have been able to outperform humans in some cases like image recognition and image classification. However, with the emergence of various novel categories, the ability to continuously widen the learning capability of such networks from limited samples, still remains a challenge. Techniques like Meta-Learning and/or few-shot learning showed promising results, where they can learn or generalize to a novel category/task based on prior knowledge. In this paper, we perform a study of the existing few-shot meta-learning techniques in the computer vision domain based on their method and evaluation metrics. We provide a taxonomy for the techniques and categorize them as data-augmentation, embedding, optimization and semantics based learning for few-shot, one-shot and zero-shot settings. We then describe the seminal work done in each category and discuss their approach towards solving the predicament of learning from few samples. Lastly we provide a comparison of these techniques on the commonly used benchmark datasets: Omniglot, and MiniImagenet, along with a discussion towards the future direction of improving the performance of these techniques towards the final goal of outperforming humans.
Few-shot Learning aims to learn classifiers for new classes with only a few training examples per class. Existing meta-learning or metric-learning based few-shot learning approaches are limited in handling diverse domains with various number of labels. The meta-learning approaches train a meta learner to predict weights of homogeneous-structured task-specific networks, requiring a uniform number of classes across tasks. The metric-learning approaches learn one task-invariant metric for all the tasks, and they fail if the tasks diverge. We propose to deal with these limitations with meta metric learning. Our meta metric learning approach consists of task-specific learners, that exploit metric learning to handle flexible labels, and a meta learner, that discovers good parameters and gradient decent to specify the metrics in task-specific learners. Thus the proposed model is able to handle unbalanced classes as well as to generate task-specific metrics. We test our approach in the `$k$-shot $N$-way' few-shot learning setting used in previous work and new realistic few-shot setting with diverse multi-domain tasks and flexible label numbers. Experiments show that our approach attains superior performances in both settings.
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