Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the r\^ole played by piecewise affine and convex nonlinearities like the ReLU and absolute value activation functions and max-pooling. In particular, DN layers constructed from these operations can be interpreted as {\em max-affine spline operators} (MASOs) that have an elegant link to vector quantization (VQ) and $K$-means. While this is good theoretical progress, the entire MASO approach is predicated on the requirement that the nonlinearities be piecewise affine and convex, which precludes important activation functions like the sigmoid, hyperbolic tangent, and softmax. {\em This paper extends the MASO framework to these and an infinitely large class of new nonlinearities by linking deterministic MASOs with probabilistic Gaussian Mixture Models (GMMs).} We show that, under a GMM, piecewise affine, convex nonlinearities like ReLU, absolute value, and max-pooling can be interpreted as solutions to certain natural "hard" VQ inference problems, while sigmoid, hyperbolic tangent, and softmax can be interpreted as solutions to corresponding "soft" VQ inference problems. We further extend the framework by hybridizing the hard and soft VQ optimizations to create a $\beta$-VQ inference that interpolates between hard, soft, and linear VQ inference. A prime example of a $\beta$-VQ DN nonlinearity is the {\em swish} nonlinearity, which offers state-of-the-art performance in a range of computer vision tasks but was developed ad hoc by experimentation. Finally, we validate with experiments an important assertion of our theory, namely that DN performance can be significantly improved by enforcing orthogonality in its linear filters.

Despite the exceptional performance of deep neural networks (DNNs) on various machine learning tasks such as malware detection (Saxe & Berlin, 2015), face recognition (Parkhi et al., 2015) and autonomous driving (Bojarski et al., 2016), recent studies (Szegedy et al., 2014; Goodfellow et al., 2015) have shown that deep learning models are vulnerable to misclassifying inputs, known as adversarial examples, that are crafted with targeted but visually-imperceptible perturbations. While several defense mechanisms have been proposed and empirically demonstrated to be successful against existing particular attacks (Papernot et al., 2016; Goodfellow et al., 2015), new attacks (Carlini & Wagner, 2017; Tramèr et al., 2017; Athalye et al., 2018) are repeatedly found that circumvent such defenses. To end this arm race, recent works (Wong & Kolter, 2018; Raghunathan et al., 2018; Wong et al., 2018; Wang et al., 2018) propose methods to certify examples to be robust against some specific norm-bounded adversarial perturbations for given inputs and to train models to optimize for certifiable robustness. However, all of the aforementioned methods aim at improving the overall robustness of the classifier. This means that the methods to improve robustness are designed to prevent seed examples in any class from being misclassified as any other classes. Achieving such a goal requires producing a perfect classifier, and has, unsurprisingly, remained elusive. Indeed, Mahloujifar et al. (2018) proved that if the metric probability space is concentrated, overall adversarial robustness is unattainable for any classifier with initial constant error. We argue that overall robustness may not be the appropriate criteria for measuring system performance in securitysensitive applications, since only certain kinds of adversarial misclassifications pose meaningful threats or provide value for adversaries.

Many transformations in deep learning architectures are sparsely connected. When such transformations cannot be designed by hand, they can be learned, even through plain backpropagation, for instance in attention mechanisms. However, during learning, such sparse structures are often represented in a dense form, as we do not know beforehand which elements will eventually become non-zero. We introduce the adaptive, sparse hyperlayer, a method for learning a sparse transformation, paramatrized sparsely: as index-tuples with associated values. To overcome the lack of gradients from such a discrete structure, we introduce a method of randomly sampling connections, and backpropagating over the randomly wired computation graph. To show that this approach allows us to train a model to competitive performance on real data, we use it to build two architectures. First, an attention mechanism for visual classification. Second, we implement a method for differentiable sorting: specifically, learning to sort unlabeled MNIST digits, given only the correct order.

We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. In order to achieve this, we propose a novel alternating random walk strategy to generate training samples from the directed graph while preserving the role information. These samples are then trained using Skip-Gram with Negative Sampling (SGNS) with nodes retaining their source/target semantics. We conduct extensive experimental evaluation to showcase our effectiveness on several real-world datasets on link prediction, multi-label classification and graph reconstruction tasks. We show that the embeddings from our approach are indeed robust, generalizable and well performing across multiple kinds of tasks and networks. We show that we consistently outperform all random-walk based neural embedding methods for link prediction and graph reconstruction tasks. In addition to providing a theoretical interpretation of our method we also show that we are more considerably robust than the other directed graph approaches.

We propose a training method for deep neural network (DNN)-based source enhancement to increase objective sound quality assessment (OSQA) scores such as the perceptual evaluation of speech quality (PESQ). In many conventional studies, DNNs have been used as a mapping function to estimate time-frequency masks and trained to minimize an analytically tractable objective function such as the mean squared error (MSE). Since OSQA scores have been used widely for sound-quality evaluation, constructing DNNs to increase OSQA scores would be better than using the minimum-MSE to create high-quality output signals. However, since most OSQA scores are not analytically tractable, \textit{i.e.}, they are black boxes, the gradient of the objective function cannot be calculated by simply applying back-propagation. To calculate the gradient of the OSQA-based objective function, we formulated a DNN optimization scheme on the basis of \textit{black-box optimization}, which is used for training a computer that plays a game. For a black-box-optimization scheme, we adopt the policy gradient method for calculating the gradient on the basis of a sampling algorithm. To simulate output signals using the sampling algorithm, DNNs are used to estimate the probability density function of the output signals that maximize OSQA scores. The OSQA scores are calculated from the simulated output signals, and the DNNs are trained to increase the probability of generating the simulated output signals that achieve high OSQA scores. Through several experiments, we found that OSQA scores significantly increased by applying the proposed method, even though the MSE was not minimized.

A neural network deployed in the wild may be asked to make predictions for inputs that were drawn from a different distribution than that of the training data. A plethora of work has demonstrated that it is easy to find or synthesize inputs for which a neural network is highly confident yet wrong. Generative models are widely viewed to be robust to such mistaken confidence as modeling the density of the input features can be used to detect novel, out-of-distribution inputs. In this paper we challenge this assumption. We find that the model density from flow-based models, VAEs and PixelCNN cannot distinguish images of common objects such as dogs, trucks, and horses (i.e. CIFAR-10) from those of house numbers (i.e. SVHN), assigning a higher likelihood to the latter when the model is trained on the former. We focus our analysis on flow-based generative models in particular since they are trained and evaluated via the exact marginal likelihood. We find such behavior persists even when we restrict the flow models to constant-volume transformations. These transformations admit some theoretical analysis, and we show that the difference in likelihoods can be explained by the location and variances of the data and the model curvature, which shows that such behavior is more general and not just restricted to the pairs of datasets used in our experiments. Our results caution against using the density estimates from deep generative models to identify inputs similar to the training distribution, until their behavior on out-of-distribution inputs is better understood.

This paper proposes a novel optimization principle and its implementation for unsupervised anomaly detection in sound (ADS) using an autoencoder (AE). The goal of unsupervised-ADS is to detect unknown anomalous sound without training data of anomalous sound. Use of an AE as a normal model is a state-of-the-art technique for unsupervised-ADS. To decrease the false positive rate (FPR), the AE is trained to minimize the reconstruction error of normal sounds and the anomaly score is calculated as the reconstruction error of the observed sound. Unfortunately, since this training procedure does not take into account the anomaly score for anomalous sounds, the true positive rate (TPR) does not necessarily increase. In this study, we define an objective function based on the Neyman-Pearson lemma by considering ADS as a statistical hypothesis test. The proposed objective function trains the AE to maximize the TPR under an arbitrary low FPR condition. To calculate the TPR in the objective function, we consider that the set of anomalous sounds is the complementary set of normal sounds and simulate anomalous sounds by using a rejection sampling algorithm. Through experiments using synthetic data, we found that the proposed method improved the performance measures of ADS under low FPR conditions. In addition, we confirmed that the proposed method could detect anomalous sounds in real environments.

This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop novel orthogonality regularizations on training deep CNNs, utilizing various advanced analytical tools such as mutual coherence and restricted isometry property. These plug-and-play regularizations can be conveniently incorporated into training almost any CNN without extra hassle. We then benchmark their effects on state-of-the-art models: ResNet, WideResNet, and ResNeXt, on several most popular computer vision datasets: CIFAR-10, CIFAR-100, SVHN and ImageNet. We observe consistent performance gains after applying those proposed regularizations, in terms of both the final accuracies achieved, and faster and more stable convergences. We have made our codes and pre-trained models publicly available: https://github.com/nbansal90/Can-we-Gain-More-from-Orthogonality.

As the technology is advancing, audio recognition in machine learning is improved as well. Research in audio recognition has traditionally focused on speech. Living creatures (especially the small ones) are part of the whole ecosystem, monitoring as well as maintaining them are important tasks. Species such as animals and birds are tending to change their activities as well as their habitats due to the adverse effects on the environment or due to other natural or man-made calamities. For those in far deserted areas, we will not have any idea about their existence until we can continuously monitor them. Continuous monitoring will take a lot of hard work and labor. If there is no continuous monitoring, then there might be instances where endangered species may encounter dangerous situations. The best way to monitor those species are through audio recognition. Classifying sound can be a difficult task even for humans. Powerful audio signals and their processing techniques make it possible to detect audio of various species. There might be many ways wherein audio recognition can be done. We can train machines either by pre-recorded audio files or by recording them live and detecting them. The audio of species can be detected by removing all the background noise and echoes. Smallest sound is considered as a syllable. Extracting various syllables is the process we are focusing on which is known as audio recognition in terms of Machine Learning (ML).

Learning to cooperate is crucially important in multi-agent reinforcement learning. The key is to take the influence of other agents into consideration when performing distributed decision making. However, multi-agent environment is highly dynamic, which makes it hard to learn abstract representations of influences between agents by only low-order features that existing methods exploit. In this paper, we propose a graph convolutional model for multi-agent cooperation. The graph convolution architecture adapts to the dynamics of the underlying graph of the multi-agent environment, where the influence among agents is captured by their abstract relation representations. High-order features extracted by relation kernels of convolutional layers from gradually increased receptive fields are exploited to learn cooperative strategies. The gradient of an agent not only backpropagates to itself but also to other agents in its receptive fields to reinforce the learned cooperative strategies. Moreover, the relation representations are temporally regularized to make the cooperation more consistent. Empirically, we show that our model enables agents to develop more cooperative and sophisticated strategies than existing methods in jungle and battle games and routing in packet switching networks.