Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and prevents the network from overfitting. In this work, we introduce the gradient gap deviation and the gradient deflection as statistical measures corresponding to the network curvature and the Hessian matrix to analyze variations of network derivatives with respect to input parameters, and investigate how implicit regularization works in ReLU neural networks from both theoretical and empirical perspectives. Our result reveals that the network output between each pair of input samples is properly controlled by random initialization and stochastic gradient descent to keep interpolating between samples almost straight, which results in low complexity of over-parameterized neural networks.

Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the information cannot be represented well enough and may lose the accuracy. This paper proposes a novel approach to enhance the data-adaptive capability for OMP-based sparse subspace clustering. In our method a parameter selection process is developed to adjust the parameters based on the data distribution for information representation. Our theoretical analysis indicates that the parameter selection process can efficiently coordinate with any OMP-based methods to improve the clustering performance. Also a new Self-Expressive-Affinity (SEA) ratio metric is defined to measure the sparse representation conversion efficiency for spectral clustering to obtain data segmentations. Experiments show that our approach achieves better performances compared with other OMP-based sparse subspace clustering algorithms in terms of clustering accuracy, SEA ratio and representation quality, and keeps the time efficiency and anti-noise ability.

In this paper,we develop a theory of the relationship between permutation ($S_n$-) invariant/equivariant functions and deep neural networks. As a result, we prove an permutation invariant/equivariant version of the universal approximation theorem, i.e $S_n$-invariant/equivariant deep neural networks. The equivariant models are consist of stacking standard single-layer neural networks $Z_i:X \to Y$ for which every $Z_i$ is $S_n$-equivariant with respect to the actions of $S_n$ . The invariant models are consist of stacking equivariant models and standard single-layer neural networks $Z_i:X \to Y$ for which every $Z_i$ is $S_n$-invariant with respect to the actions of $S_n$ . These are universal approximators to $S_n$-invariant/equivariant functions. The above notation is mathematically natural generalization of the models in \cite{deepsets}. We also calculate the number of free parameters appeared in these models. As a result, the number of free parameters appeared in these models is much smaller than the one of the usual models. Hence, we conclude that although the free parameters of the invariant/equivarint models are exponentially fewer than the one of the usual models, the invariant/equivariant models can approximate the invariant/equivariant functions to arbitrary accuracy. This gives us an understanding of why the invariant/equivariant models designed in [Zaheer et al. 2018] work well.

A Pathology report is arguably one of the most important documents in medicine containing interpretive information about the visual findings from the patient's biopsy sample. Each pathology report has a retention period of up to 20 years after the treatment of a patient. Cancer registries process and encode high volumes of free-text pathology reports for surveillance of cancer and tumor diseases all across the world. In spite of their extremely valuable information they hold, pathology reports are not used in any systematic way to facilitate computational pathology. Therefore, in this study, we investigate automated machine-learning techniques to identify/predict the primary diagnosis (based on ICD-O code) from pathology reports. We performed experiments by extracting the TF-IDF features from the reports and classifying them using three different methods---SVM, XGBoost, and Logistic Regression. We constructed a new dataset with 1,949 pathology reports arranged into 37 ICD-O categories, collected from four different primary sites, namely lung, kidney, thymus, and testis. The reports were manually transcribed into text format after collecting them as PDF files from NCI Genomic Data Commons public dataset. We subsequently pre-processed the reports by removing irrelevant textual artifacts produced by OCR software. The highest classification accuracy we achieved was 92\% using XGBoost classifier on TF-IDF feature vectors, the linear SVM scored 87\% accuracy. Furthermore, the study shows that TF-IDF vectors are suitable for highlighting the important keywords within a report which can be helpful for the cancer research and diagnostic workflow. The results are encouraging in demonstrating the potential of machine learning methods for classification and encoding of pathology reports.

The game of bridge consists of two stages: bidding and playing. While playing is proved to be relatively easy for computer programs, bidding is very challenging. During the bidding stage, each player knowing only his/her own cards needs to exchange information with his/her partner and interfere with opponents at the same time. Existing methods for solving perfect-information games cannot be directly applied to bidding. Most bridge programs are based on human-designed rules, which, however, cannot cover all situations and are usually ambiguous and even conflicting with each other. In this paper, we, for the first time, propose a competitive bidding system based on deep learning techniques, which exhibits two novelties. First, we design a compact representation to encode the private and public information available to a player for bidding. Second, based on the analysis of the impact of other players' unknown cards on one's final rewards, we design two neural networks to deal with imperfect information, the first one inferring the cards of the partner and the second one taking the outputs of the first one as part of its input to select a bid. Experimental results show that our bidding system outperforms the top rule-based program.

Active localization is the problem of generating robot actions that allow it to maximally disambiguate its pose within a reference map. Traditional approaches to this use an information-theoretic criterion for action selection and hand-crafted perceptual models. In this work we propose an end-to-end differentiable method for learning to take informative actions that is trainable entirely in simulation and then transferable to real robot hardware with zero refinement. The system is composed of two modules: a convolutional neural network for perception, and a deep reinforcement learned planning module. We introduce a multi-scale approach to the learned perceptual model since the accuracy needed to perform action selection with reinforcement learning is much less than the accuracy needed for robot control. We demonstrate that the resulting system outperforms using the traditional approach for either perception or planning. We also demonstrate our approaches robustness to different map configurations and other nuisance parameters through the use of domain randomization in training. The code is also compatible with the OpenAI gym framework, as well as the Gazebo simulator.

Numerous past works have tackled the problem of task-driven navigation. But, how to effectively explore a new environment to enable a variety of downstream tasks has received much less attention. In this work, we study how agents can autonomously explore realistic and complex 3D environments without the context of task-rewards. We propose a learning-based approach and investigate different policy architectures, reward functions, and training paradigms. We find that use of policies with spatial memory that are bootstrapped with imitation learning and finally finetuned with coverage rewards derived purely from on-board sensors can be effective at exploring novel environments. We show that our learned exploration policies can explore better than classical approaches based on geometry alone and generic learning-based exploration techniques. Finally, we also show how such task-agnostic exploration can be used for downstream tasks. Imagine your first day at a new workplace. If you are like most people, the first task you set for yourself is to become familiar with the office so that the next day when you have to attend meetings and perform tasks, you can navigate efficiently and seamlessly. To achieve that goal, you explore your office without the task context of target locations you have to reach and build a generic understanding of space. This step of task-independent exploration is quite critical yet often ignored in current approaches for navigation. When it comes to navigation, currently there are two paradigms: (a) geometric reconstruction and path-planning based approaches (Hartley & Zisserman, 2003; Thrun et al., 2005; LaValle, 2006), and (b) learning-based approaches (Mirowski et al., 2017; Gupta et al., 2017; Savinov et al., 2018; Zhu et al., 2017).

Cloud computing data centers are growing in size and complexity to the point where monitoring and management of the infrastructure become a challenge due to scalability issues. A possible approach to cope with the size of such data centers is to identify VMs exhibiting a similar behavior. Existing literature demonstrated that clustering together VMs that show a similar behavior may improve the scalability of both monitoring andmanagement of a data center. However, available techniques suffer from a trade-off between accuracy and time to achieve this result. Throughout this paper we propose a different approach where, instead of an unsupervised clustering, we rely on classifiers based on deep learning techniques to assigna newly deployed VMs to a cluster of already-known VMs. The two proposed classifiers, namely DeepConv and DeepFFT use a convolution neural network and (in the latter model) exploits Fast Fourier Transformation to classify the VMs. Our proposal is validated using a set of traces describing the behavior of VMs from a realcloud data center. The experiments compare our proposal with state-of-the-art solutions available in literature, demonstrating that our proposal achieve better performance. Furthermore, we show that our solution issignificantly faster than the alternatives as it can produce a perfect classification even with just a few samples of data, making our proposal viable also toclassify on-demand VMs that are characterized by a short life span.

We present the first application of deep learning at scale to do gravitational wave parameter estimation of binary black hole mergers that describe a 4-D signal manifold, i.e., black holes whose spins are aligned or anti-aligned, and which evolve on quasi-circular orbits. We densely sample this 4-D signal manifold using over three hundred thousand simulated waveforms. In order to cover a broad range of astrophysically motivated scenarios, we synthetically enhance this waveform dataset to ensure that our deep learning algorithms can process waveforms located at any point in the data stream of gravitational wave detectors (time invariance) for a broad range of signal-to-noise ratios (scale invariance), which in turn means that our neural network models are trained with over $10^{7}$ waveform signals. We then apply these neural network models to estimate the astrophysical parameters of black hole mergers, and their corresponding black hole remnants, including the final spin and the gravitational wave quasi-normal frequencies. These neural network models represent the first time deep learning is used to provide point-parameter estimation calculations endowed with statistical errors. For each binary black hole merger that ground-based gravitational wave detectors have observed, our deep learning algorithms can reconstruct its parameters within 2 milliseconds using a single Tesla V100 GPU. We show that this new approach produces parameter estimation results that are consistent with Bayesian analyses that have been used to reconstruct the parameters of the catalog of binary black hole mergers observed by the advanced LIGO and Virgo detectors.

Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account only the properties related to the intrinsic logical soundness of an argument in order to determine its acceptability status. However, these properties are not always the only ones that matter to establish the argument's acceptability---there exist other qualities, such as strength, weight, social votes, trust degree, relevance level, and certainty degree, among others.