A Group Theoretic Perspective on Unsupervised Deep Learning
Intel Corporation（英特尔公司）；University of Utah（犹他大学）
Arnab Paul, Suresh Venkatasubramanian
备注：
2-page version of arXiv:1412.6621 prepared for presentation at ICLR 2015 workshop as required by ICLR PC). This version has some minor formatting changes as required by the conference
Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.
One factor behind the recent resurgence of the subject is a key algorithmic step called {\em pretraining}: first search for a good generative model for the input samples, and repeat the process one layer at a time. We show deeper implications of this simple principle, by establishing a connection with the interplay of orbits and stabilizers of group actions. Although the neural networks themselves may not form groups, we show the existence of {\em shadow} groups whose elements serve as close approximations.
Over the shadow groups, the pre-training step, originally introduced as a mechanism to better initialize a network, becomes equivalent to a search for features with minimal orbits. Intuitively, these features are in a way the {\em simplest}. Which explains why a deep learning network learns simple features first. Next, we show how the same principle, when repeated in the deeper layers, can capture higher order representations, and why representation complexity increases as the layers get deeper.
Model identifiability is a desirable property in the context of unsupervised representation learning. In absence thereof, different models may be observationally indistinguishable while yielding representations that are nontrivially related to one another, thus making the recovery of a ground truth generative model fundamentally impossible, as often shown through suitably constructed counterexamples. In this note, we discuss one such construction, illustrating a potential failure case of an identifiability result presented in "Desiderata for Representation Learning: A Causal Perspective" by Wa…
Location is key to spatialize internet-of-things (IoT) data. However, it is challenging to use low-cost IoT devices for robust unsupervised localization (i.e., localization without training data that have known location labels). Thus, this paper proposes a deep reinforcement learning (DRL) based unsupervised wireless-localization method. The main contributions are as follows. (1) This paper proposes an approach to model a continuous wireless-localization process as a Markov decision process (MDP) and process it within a DRL framework. (2) To alleviate the challenge of obtaining rewards when us…
Content delivery networks (CDNs) provide efficient content distribution over the Internet. CDNs improve the connectivity and efficiency of global communications, but their caching mechanisms may be breached by cyber-attackers. Among the security mechanisms, effective anomaly detection forms an important part of CDN security enhancement. In this work, we propose a multi-perspective unsupervised learning framework for anomaly detection in CDNs. In the proposed framework, a multi-perspective feature engineering approach, an optimized unsupervised anomaly detection model that utilizes an isolation…
The ability to recognize objects despite there being differences in appearance, known as Core Object Recognition, forms a critical part of human perception. While it is understood that the brain accomplishes Core Object Recognition through feedforward, hierarchical computations through the visual stream, the underlying algorithms that allow for invariant representations to form downstream is still not well understood. (DiCarlo et al., 2012) Various computational perceptual models have been built to attempt and tackle the object identification task in an artificial perceptual setting. Artificia…
Difficult Examples Hurt Unsupervised Contrastive Learning: A Theoretical Perspective
State Key Lab of General AI, School of Intelligence Science and Technology, Peking University（北京大学智能科学与技术学院人工智能国家重点实验室）；School of Engineering, Hong Kong University of Science and Technology（香港科技大学工程学院）；Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）
We investigate the effects of the unsupervised pre-training method under the perspective of information theory. If the input distribution displays multiple views of the supervision, then unsupervised pre-training allows to learn hierarchical representation which communicates these views across layers, while disentangling the supervision. Disentanglement of supervision leads learned features to be independent conditionally to the label. In case of binary features, we show that conditional independence allows to extract label's information with a linear model and therefore helps to solve under-f…
We study the problem of unsupervised domain adaptation, which aims to adapt classifiers trained on a labeled source domain to an unlabeled target domain. Many existing approaches first learn domain-invariant features and then construct classifiers with them. We propose a novel approach that jointly learn the both. Specifically, while the method identifies a feature space where data in the source and the target domains are similarly distributed, it also learns the feature space discriminatively, optimizing an information-theoretic metric as an proxy to the expected misclassification error on th…
University of International Business and Economics（对外经济贸易大学）
Unsupervised contrastive learning has gained increasing attention in the latest research and has proven to be a powerful method for learning representations from unlabeled data. However, little theoretical analysis was known for this framework. In this paper, we study the optimization of deep unsupervised contrastive learning. We prove that, by applying end-to-end training that simultaneously updates two deep over-parameterized neural networks, one can find an approximate stationary solution for the non-convex contrastive loss. This result is inherently different from the existing over-paramet…
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Ewha Womans University（梨花女子大学）
Deep learning has become the method of choice to tackle real-world problems in different domains, partly because of its ability to learn from data and achieve impressive performance on a wide range of applications. However, its success usually relies on two assumptions: (i) vast troves of labeled datasets are required for accurate model fitting, and (ii) training and testing data are independent and identically distributed. Its performance on unseen target domains, thus, is not guaranteed, especially when encountering out-of-distribution data at the adaptation stage. The performance drop on da…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a central theme in deep learning with important applications in computer vision and computational neuroscience. In this article, we review recent advances in learning representations from a statistical perspective. In particular, we review the following two themes: (a) unsupervised learning of vector representations and (b) learning of both vector and matrix repre…
Revisiting VAE for Unsupervised Time Series Anomaly Detection: A Frequency Perspective
University of Chinese Academy of Sciences（中国科学院大学）；Computer Network Information Center, Chinese Academy of Sciences（中国科学院计算机网络信息中心）；Microsoft（微软公司）；Stony Brook University（石溪大学）；Kuaishou Technology（快手科技）；Tsinghua University（清华大学）
Shanghai Jiao Tong University（上海交通大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Surrogate task based methods have recently shown great promise for unsupervised image anomaly detection. However, there is no guarantee that the surrogate tasks share the consistent optimization direction with anomaly detection. In this paper, we return to a direct objective function for anomaly detection with information theory, which maximizes the distance between normal and anomalous data in terms of the joint distribution of images and their representation. Unfortunately, this objective function is not directly optimizable under the unsupervised setting where no anomalous data is provided …
School of Software, BNRist, Research Center for Big Data, Tsinghua University（清华大学软件学院、北京智源人工智能研究院、大数据研究中心）
This paper explores a new research problem of unsupervised transfer learning across multiple spatiotemporal prediction tasks. Unlike most existing transfer learning methods that focus on fixing the discrepancy between supervised tasks, we study how to transfer knowledge from a zoo of unsupervisedly learned models towards another predictive network. Our motivation is that models from different sources are expected to understand the complex spatiotemporal dynamics from different perspectives, thereby effectively supplementing the new task, even if the task has sufficient training samples. Techni…
This paper uses information-theoretic tools to analyze the generalization error in unsupervised domain adaptation (UDA). We present novel upper bounds for two notions of generalization errors. The first notion measures the gap between the population risk in the target domain and that in the source domain, and the second measures the gap between the population risk in the target domain and the empirical risk in the source domain. While our bounds for the first kind of error are in line with the traditional analysis and give similar insights, our bounds on the second kind of error are algorithm-…
Johns Hopkins University School of Medicine（约翰斯·霍普金斯大学医学院）
A framework is presented for unsupervised learning of representations based on infomax principle for large-scale neural populations. We use an asymptotic approximation to the Shannon's mutual information for a large neural population to demonstrate that a good initial approximation to the global information-theoretic optimum can be obtained by a hierarchical infomax method. Starting from the initial solution, an efficient algorithm based on gradient descent of the final objective function is proposed to learn representations from the input datasets, and the method works for complete, overcompl…
Stanford University（斯坦福大学）；Cornell University（康奈尔大学）；Brain of Things
Supervised learning with large scale labeled datasets and deep layered models has made a paradigm shift in diverse areas in learning and recognition. However, this approach still suffers generalization issues under the presence of a domain shift between the training and the test data distribution. In this regard, unsupervised domain adaptation algorithms have been proposed to directly address the domain shift problem. In this paper, we approach the problem from a transductive perspective. We incorporate the domain shift and the transductive target inference into our framework by jointly solvin…
Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering
State Key Laboratory for Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Ant Group（蚂蚁集团）；Westlake University（西湖大学）；College of Computer Science and Technology, National University of Defense Technology（国防科技大学计算机科学与技术学院）
Joint Laboratory of Data Science and Business Intelligence, School of Statistics and Data Science, Southwestern University of Finance and Economics（数据科学与商务智能联合实验室，统计与数据科学学院，西南财经大学）；College of Information Science and Engineering, Ocean University of China（信息科学与工程学院，中国海洋大学）；School of Computing and Artificial Intelligence, Southwest Jiaotong University（计算与人工智能学院，西南交通大学）
We present a large-scale study on unsupervised spatiotemporal representation learning from videos. With a unified perspective on four recent image-based frameworks, we study a simple objective that can easily generalize all these methods to space-time. Our objective encourages temporally-persistent features in the same video, and in spite of its simplicity, it works surprisingly well across: (i) different unsupervised frameworks, (ii) pre-training datasets, (iii) downstream datasets, and (iv) backbone architectures. We draw a series of intriguing observations from this study, e.g., we discover…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；Carnegie Mellon University（卡内基梅隆大学）
Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzi…
Centre for Mathematical Sciences（数学科学中心）；Faculty of Classics（古典学系）
In this paper we introduce the ROman COmmonware POTtery (ROCOPOT) database, which comprises of more than 2000 black and white imaging profiles of pottery shapes extracted from 11 Roman catalogues and related to different excavation sites. The partiality and the handcrafted variance of the shape fragments within this new database make their unsupervised clustering a very challenging problem: profile similarities are thus explored via the hierarchical clustering of non-linear features learned in the latent representation space of a stacked sparse autoencoder (SSAE) network, unveiling new profile…
Xi’an Jiaotong University（西安交通大学）；HKUST（香港科技大学）；Microsoft Research Asia（微软亚洲研究院）；EIT（电子与信息技术研究所）
Disentangled representation learning is one of the major goals of deep learning, and is a key step for achieving explainable and generalizable models. A well-defined theoretical guarantee still lacks for the VAE-based unsupervised methods, which are a set of popular methods to achieve unsupervised disentanglement. The Group Theory based definition of representation disentanglement mathematically connects the data transformations to the representations using the formalism of group. In this paper, built on the group-based definition and inspired by the n-th dihedral group, we first propose a the…
Unsupervised neural networks, such as restricted Boltzmann machines (RBMs) and deep belief networks (DBNs), are powerful tools for feature selection and pattern recognition tasks. We demonstrate that overfitting occurs in such models just as in deep feedforward neural networks, and discuss possible regularization methods to reduce overfitting. We also propose a "partial" approach to improve the efficiency of Dropout/DropConnect in this scenario, and discuss the theoretical justification of these methods from model convergence and likelihood bounds. Finally, we compare the performance of these …
Representation learning constructs low-dimensional representations to summarize essential features of high-dimensional data. This learning problem is often approached by describing various desiderata associated with learned representations; e.g., that they be non-spurious, efficient, or disentangled. It can be challenging, however, to turn these intuitive desiderata into formal criteria that can be measured and enhanced based on observed data. In this paper, we take a causal perspective on representation learning, formalizing non-spuriousness and efficiency (in supervised representation learni…
Université de Paris（巴黎大学）；Université Paris-Dauphine（巴黎多芬纳大学）；Ecole normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）
Contrastive representation learning has been recently proved to be very efficient for self-supervised training. These methods have been successfully used to train encoders which perform comparably to supervised training on downstream classification tasks. A few works have started to build a theoretical framework around contrastive learning in which guarantees for its performance can be proven. We provide extensions of these results to training with multiple negative samples and for multiway classification. Furthermore, we provide convergence guarantees for the minimization of the contrastive t…
University of Chinese Academy of Sciences（中国科学院大学）；Information Science Academy of China Electronics Technology Group Corporation（中国电子科技集团公司信息科学研究院）
We propose a novel and theoretical model, blocked and hierarchical variational autoencoder (BHiVAE), to get better-disentangled representation. It is well known that information theory has an excellent explanatory meaning for the network, so we start to solve the disentanglement problem from the perspective of information theory. BHiVAE mainly comes from the information bottleneck theory and information maximization principle. Our main idea is that (1) Neurons block not only one neuron node is used to represent attribute, which can contain enough information; (2) Create a hierarchical structur…
Recently, deep learning approaches have become the main research frontier for biological image reconstruction and enhancement problems thanks to their high performance, along with their ultra-fast inference times. However, due to the difficulty of obtaining matched reference data for supervised learning, there has been increasing interest in unsupervised learning approaches that do not need paired reference data. In particular, self-supervised learning and generative models have been successfully used for various biological imaging applications. In this paper, we overview these approaches from…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；College of William and Mary（威廉与玛丽学院）
This paper develops a novel unsupervised algorithm for belief representation learning in polarized networks that (i) uncovers the latent dimensions of the underlying belief space and (ii) jointly embeds users and content items (that they interact with) into that space in a manner that facilitates a number of downstream tasks, such as stance detection, stance prediction, and ideology mapping. Inspired by total correlation in information theory, we propose the Information-Theoretic Variational Graph Auto-Encoder (InfoVGAE) that learns to project both users and content items (e.g., posts that rep…
Unsupervised time series clustering is a challenging problem with diverse industrial applications such as anomaly detection, bio-wearables, etc. These applications typically involve small, low-power devices on the edge that collect and process real-time sensory signals. State-of-the-art time-series clustering methods perform some form of loss minimization that is extremely computationally intensive from the perspective of edge devices. In this work, we propose a neuromorphic approach to unsupervised time series clustering based on Temporal Neural Networks that is capable of ultra low-power, co…
Investigation of age-related genes is of great importance for multiple purposes, for instance, improving our understanding of the mechanism of ageing, increasing life expectancy, age prediction, and other healthcare applications. In his work, starting with a set of 27,142 genes, we develop an information-theoretic framework for identifying genes that are associated with aging by applying unsupervised and semi-supervised learning techniques on human dermal fibroblast gene expression data. First, we use unsupervised learning and apply information-theoretic measures to identify key features for e…
The present Multi-view stereo (MVS) methods with supervised learning-based networks have an impressive performance comparing with traditional MVS methods. However, the ground-truth depth maps for training are hard to be obtained and are within limited kinds of scenarios. In this paper, we propose a novel unsupervised multi-metric MVS network, named M^3VSNet, for dense point cloud reconstruction without any supervision. To improve the robustness and completeness of point cloud reconstruction, we propose a novel multi-metric loss function that combines pixel-wise and feature-wise loss function t…
Xi’an Jiaotong University（西安交通大学）；University of Waterloo（滑铁卢大学）；University of Virginia（弗吉尼亚大学）；University of New South Wales（新南威尔士大学）；University of Technology Sydney（悉尼科技大学）
Due to the superior performance of Graph Neural Networks (GNNs) in various domains, there is an increasing interest in the GNN explanation problem "\emph{which fraction of the input graph is the most crucial to decide the model's decision?}" Existing explanation methods focus on the supervised settings, \eg, node classification and graph classification, while the explanation for unsupervised graph-level representation learning is still unexplored. The opaqueness of the graph representations may lead to unexpected risks when deployed for high-stake decision-making scenarios. In this paper, we a…
University of Tübingen（图宾根大学）；University of Surrey（萨里大学）；MPI for Informatics（马克斯·普朗克信息学研究所）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）
State-of-the-art deep learning models are often trained with a large amount of costly labeled training data. However, requiring exhaustive manual annotations may degrade the model's generalizability in the limited-label regime. Semi-supervised learning and unsupervised learning offer promising paradigms to learn from an abundance of unlabeled visual data. Recent progress in these paradigms has indicated the strong benefits of leveraging unlabeled data to improve model generalization and provide better model initialization. In this survey, we review the recent advanced deep learning algorithms …
University of Glasgow（格拉斯哥大学）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology（印度理工学院）；Durham University（杜伦大学）
Anomaly detection through employing machine learning techniques has emerged as a novel powerful tool in the search for new physics beyond the Standard Model. Historically similar to the development of jet observables, theoretical consistency has not always assumed a central role in the fast development of algorithms and neural network architectures. In this work, we construct an infrared and collinear safe autoencoder based on graph neural networks by employing energy-weighted message passing. We demonstrate that whilst this approach has theoretically favourable properties, it also exhibits fo…
