Abstract-- Self-driving technology is advancing rapidly, largely due to recent developments in deep learning algorithms. To date, however, there has been no systematic comparison of how different deep learning architectures perform at such tasks, or an attempt to determine a correlation between classification performance and performance in an actual vehicle. Here, we introduce the first controlled comparison of seven contemporary deep-learning architectures in an end-to-end autonomous driving task. We use a simple and affordable platform consisting of of an off-the-shelf, remotely operated vehicle, a GPU equipped computer and an indoor foam-rubber racetrack. We compare a fully-connected network, a 2-layer CNN, AlexNet, VGG-16, Inception-V3, ResNet-26, and LSTM and report the number of laps they are able to successfully complete without crashing while traversing an indoor racetrack under identical testing conditions. Based on these tests, AlexNet completed the most laps without crashing out of all networks, and ResNet-26 is the most'efficient' architecture examined, with respect to the number of laps completed relative to the number of parameters. We also observe whether spatial, color, or temporal features -- or some combination -- are more important for such tasks. Finally, we show that validation loss/accuracy is not sufficiently indicative of the model's performance even when employed in a real vehicle with a simple task, emphasizing the need for greater accessibility to research platforms within the selfdriving community.

Stochastic gradient descent (SGD) and its variations, e.g., SGD with either classic or Nesterov momentum, RMSProp, Adam, adaptive learning rates, etc., are popular in diverse stochastic optimization problems, e.g., machine learning and online signal processing [1]-[6]. Off-the-shelf methods from convex optimizations, e.g., the quasi-Newton method, conjugate gradient method and truncated Newton method, i.e., the Hessian-free optimization, are attracting more attentions [7]-[10], and find many successful applications in stochastic optimizations as well. At the same time, searchings for new optimization theories and learning rules are always active, and methods like natural gradient descent, relative gradient descent, and equilibrated SGD (ESGD) [11]-[13], provide us with great insight into the properties of the parameter spaces and cost function surfaces in stochastic optimizations. This paper studies the performance of preconditioned SGD (PSGD) [14], a method which explicitly considers the non-convexity and gradient noises in stochastic optimizations. We consider preconditioners in several forms, i.e., dense preconditioner, diagonal preconditioner, Kronecker product preconditioner and more flexible forms. ESGD and batch normalization [18] are shown to be PSGDs with specific forms of preconditioners. We also consider different ways to evaluate the Hessianvector product, an important measurement that helps PSGD to adaptively extract the curvature information of cost surfaces. Our benchmark problems have synthetic and real world data, and involves most commonly used neural network models, e.g., recurrent and convolutional networks. We argue that Kronecker product preconditioners are particularly suitable for training neural networks since affine transformations are their basic building blocks.

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of the transition matrix of an RNN that allows us to stabilize the gradients that arise in its training. Specifically, we parameterize the transition matrix by its singular value decomposition(SVD), which allows us to explicitly track and control its singular values. We attain efficiency by using tools that are common in numerical linear algebra, namely Householder reflectors for representing the orthogonal matrices that arise in the SVD. By explicitly controlling the singular values, our proposed Spectral-RNN method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent. We note that the SVD parameterization can be used for any rectangular weight matrix, hence it can be easily extended to any deep neural network, such as a multi-layer perceptron. Theoretically, we demonstrate that our parameterization does not lose any expressive power, and show how it controls generalization of RNN for the classification task. %, and show how it potentially makes the optimization process easier. Our extensive experimental results also demonstrate that the proposed framework converges faster, and has good generalization, especially in capturing long range dependencies, as shown on the synthetic addition and copy tasks, as well as on MNIST and Penn Tree Bank data sets.

Deep neural networks, in particular generative adversarial networks by [Goodfellow et al., 2014] have been recently used to produce generative models for real world data that can capture very complex structures. This is especially true for natural images (see for instance [Nguyen et al., 2016]). Those generative priors have been successfully used to efficiently solve classical inverse problems in signal processing, like super resolution ([Johnson et al., 2016]) and compressed sensing ([Bora et al., 2017]). The latter numerically demonstrates that the generative prior can be exploited to solve the compressed sensing problem with ten times fewer measurements than the classic compressed sensing theory requires. Followup work by [Hand and Voroninski, 2017] recently explained the success of local methods (namely empirical risk minimization) in the compressed sensing task by assuming a generative model of a multi-layer neural network with random weights and ReLU activation functions. The aim of this paper is to propose a theoretical framework that will allow us to analyze neural networks in the context of another classical inverse problem in signal processing: signal denoising.

Goldbach conjecture is one of the most famous open mathematical problems. It states that every even number, bigger than two, can be presented as a sum of 2 prime numbers. In this work we present a deep learning based model that predicts the number of Goldbach partitions for a given even number. Surprisingly, our model outperforms all state-of-the-art analytically derived estimations for the number of couples, while not requiring prime factorization of the given number. We believe that building a model that can accurately predict the number of couples brings us one step closer to solving one of the world most famous open problems. To the best of our knowledge, this is the first attempt to consider machine learning based datadriven methods to approximate open mathematical problems in the field of number theory, and hope that this work will encourage such attempts.

Recent advances in video super-resolution have shown that convolutional neural networks combined with motion compensation are able to merge information from multiple low-resolution (LR) frames to generate high-quality images. Current state-of-the-art methods process a batch of LR frames to generate a single high-resolution (HR) frame and run this scheme in a sliding window fashion over the entire video, effectively treating the problem as a large number of separate multi-frame super-resolution tasks. This approach has two main weaknesses: 1) Each input frame is processed and warped multiple times, increasing the computational cost, and 2) each output frame is estimated independently conditioned on the input frames, limiting the system's ability to produce temporally consistent results. In this work, we propose an end-to-end trainable frame-recurrent video super-resolution framework that uses the previously inferred HR estimate to super-resolve the subsequent frame. This naturally encourages temporally consistent results and reduces the computational cost by warping only one image in each step. Furthermore, due to its recurrent nature, the proposed method has the ability to assimilate a large number of previous frames without increased computational demands. Extensive evaluations and comparisons with previous methods validate the strengths of our approach and demonstrate that the proposed framework is able to significantly outperform the current state of the art.

Malware is constantly adapting in order to avoid detection. Model based malware detectors, such as SVM and neural networks, are vulnerable to so-called adversarial examples which are modest changes to detectable malware that allows the resulting malware to evade detection. Continuous-valued methods that are robust to adversarial examples of images have been developed using saddle-point optimization formulations. We are inspired by them to develop similar methods for the discrete, e.g. binary, domain which characterizes the features of malware. A specific extra challenge of malware is that the adversarial examples must be generated in a way that preserves their malicious functionality. We introduce methods capable of generating functionally preserved adversarial malware examples in the binary domain. Using the saddle-point formulation, we incorporate the adversarial examples into the training of models that are robust to them. We evaluate the effectiveness of the methods and others in the literature on a set of Portable Execution~(PE) files. Comparison prompts our introduction of an online measure computed during training to assess general expectation of robustness.

Recent advances in policy gradient methods and deep learning have demonstrated their applicability for complex reinforcement learning problems. However, the variance of the performance gradient estimates obtained from the simulation is often excessive, leading to poor sample efficiency. In this paper, we apply the stochastic variance reduced gradient descent (SVRG) to model-free policy gradient to significantly improve the sample-efficiency. The SVRG estimation is incorporated into a trust-region Newton conjugate gradient framework for the policy optimization. On several Mujoco tasks, our method achieves significantly better performance compared to the state-of-the-art model-free policy gradient methods in robotic continuous control such as trust region policy optimization (TRPO)

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack the ability of tractable marginalization, and thus are not suitable for many tasks. Other methods, based on arithmetic circuits and sum-product networks, do allow tractable marginalization, but their performance is challenged by the need to learn the structure of a circuit. Building on the tractability of arithmetic circuits, we leverage concepts from tensor analysis, and derive a family of generative models we call Tensorial Mixture Models (TMMs). TMMs assume a simple convolutional network structure, and in addition, lend themselves to theoretical analyses that allow comprehensive understanding of the relation between their structure and their expressive properties. We thus obtain a generative model that is tractable on one hand, and on the other hand, allows effective representation of rich distributions in an easily controlled manner. These two capabilities are brought together in the task of classification under missing data, where TMMs deliver state of the art accuracies with seamless implementation and design.

World Bank hosted its poverty prediction competition on the competition hosting website drivendata.org. The link to the competition is here. We decided to try out our Machine Learning skills on this dataset. Most regular work in ParallelDots is around three themes: Visual Analytics on images and videos, Healthcare AI and NLP, all three of which are solved using Deep Learning techniques. This competition was a chance to try out something new and build our internal codebase to handle tabular datasets like what we had in the competition.