Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ adversarial training to improve the performance of randomized smoothing. We design an adapted attack for smoothed classifiers, and we show how this attack can be used in an adversarial training setting to boost the provable robustness of smoothed classifiers. We demonstrate through extensive experimentation that our method consistently outperforms all existing provably $\ell_2$-robust classifiers by a significant margin on ImageNet and CIFAR-10, establishing the state-of-the-art for provable $\ell_2$-defenses. Our code and trained models are available at http://github.com/Hadisalman/smoothing-adversarial .

A series of recent works suggest that deep neural networks (DNNs), of fixed depth, are equivalent to certain Gaussian Processes (NNGP/NTK) in the highly over-parameterized regime (width or number-of-channels going to infinity). Other works suggest that this limit is relevant for real-world DNNs. These results invite further study into the generalization properties of Gaussian Processes of the NNGP and NTK type. Here we make several contributions along this line. First, we develop a formalism, based on field theory tools, for calculating learning curves perturbatively in one over the dataset size. For the case of NNGPs, this formalism naturally extends to finite width corrections. Second, in cases where one can diagonalize the covariance-function of the NNGP/NTK, we provide analytic expressions for the asymptotic learning curves of any given target function. These go beyond the standard equivalence kernel results. Last, we provide closed analytic expressions for the eigenvalues of NNGP/NTK kernels of depth 2 fully-connected ReLU networks. For datasets on the hypersphere, the eigenfunctions of such kernels, at any depth, are hyperspherical harmonics. A simple coherent picture emerges wherein fully-connected DNNs have a strong entropic bias towards functions which are low order polynomials of the input.

Recently, natural policy gradient algorithms gained widespread recognition due to their strong performance in reinforcement learning tasks [12, 13]. However, their major drawback is the need to secure the policy being in a "trust region" and meanwhile allowing for sufficient exploration. The main objective of this study was to present an approach which models dynamical isometry of agents policies by estimating conditioning of its Jacobian at individual points in the environment space. We present a Jacobian Policy Optimization algorithm for policy optimization, which dynamically adapts the trust interval with respect to policy conditioning. The suggested approach was tested across a range of Atari environments. This paper offers some important insights into an improvement of policy optimization in reinforcement learning tasks.

In this work we aim to obtain computationally-efficient uncertainty estimates with deep networks. For this, we propose a modified knowledge distillation procedure that achieves state-of-the-art uncertainty estimates both for in and out-of-distribution samples. Our contributions include a) demonstrating and adapting to distillation's regularization effect b) proposing a novel target teacher distribution c) a simple augmentation procedure to improve out-of-distribution uncertainty estimates d) shedding light on the distillation procedure through comprehensive set of experiments.

We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variational inference on this construction enables a sampling-free computation of the evidence lower bound which is a more effective approximation than the widely applied Monte Carlo sampling and CLT related techniques. We evaluate the model on a range of regression and classification tasks against BNN inference alternatives, showing competitive or improved performance over the current state-of-the-art.

Time series are ubiquitous in real world problems and computing distance between two time series is often required in several learning tasks. Computing similarity between time series by ignoring variations in speed or warping is often encountered and dynamic time warping (DTW) is the state of the art. However DTW is not applicable in algorithms which require kernel or vectors. In this paper, we propose a mechanism named WaRTEm to generate vector embeddings of time series such that distance measures in the embedding space exhibit resilience to warping. Therefore, WaRTEm is more widely applicable than DTW. WaRTEm is based on a twin auto-encoder architecture and a training strategy involving warping operators for generating warping resilient embeddings for time series datasets. We evaluate the performance of WaRTEm and observed more than $20\%$ improvement over DTW in multiple real-world datasets.

Determining an appropriate number of features for each layer in a neural network is an important and difficult task. This task is especially important in applications on systems with limited memory or processing power. Many current approaches to reduce network size either utilize iterative procedures, which can extend training time significantly, or require very careful tuning of algorithm parameters to achieve reasonable results. In this paper we propose NodeDrop, a new method for eliminating features in a network. With NodeDrop, we define a condition to identify and guarantee which nodes carry no information, and then use regularization to encourage nodes to meet this condition. We find that NodeDrop drastically reduces the number of features in a network while maintaining high performance, reducing the number of parameters by a factor of 114x for a VGG like network on CIFAR10 without a drop in accuracy.

Single image de-raining is an extremely challenging problem since the rainy image may contain rain streaks which may vary in size, direction and density. Previous approaches have attempted to address this problem by leveraging some prior information to remove rain streaks from a single image. One of the major limitations of these approaches is that they do not consider the location information of rain drops in the image. The proposed Uncertainty guided Multi-scale Residual Learning (UMRL) network attempts to address this issue by learning the rain content at different scales and using them to estimate the final de-rained output. In addition, we introduce a technique which guides the network to learn the network weights based on the confidence measure about the estimate. Furthermore, we introduce a new training and testing procedure based on the notion of cycle spinning to improve the final de-raining performance. Extensive experiments on synthetic and real datasets to demonstrate that the proposed method achieves significant improvements over the recent state-of-the-art methods. Code is available at: https://github.com/rajeevyasarla/UMRL--using-Cycle-Spinning

Handwriting disorder (termed dysgraphia) is a far from a singular problem as nearly 8.6% of the population in France is considered dysgraphic. Moreover, research highlights the fundamental importance to detect and remediate these handwriting difficulties as soon as possible as they may affect a child's entire life, undermining performance and self-confidence in a wide variety of school activities. At the moment, the detection of handwriting difficulties is performed through a standard test called BHK. This detection, performed by therapists, is laborious because of its high cost and subjectivity. We present a digital approach to identify and characterize handwriting difficulties via a Recurrent Neural Network model (RNN). The child under investigation is asked to write on a graphics tablet all the letters of the alphabet as well as the ten digits. Once complete, the RNN delivers a diagnosis in a few milliseconds and demonstrates remarkable efficiency as it correctly identifies more than 90% of children diagnosed as dysgraphic using the BHK test. The main advantage of our tablet-based system is that it captures the dynamic features of writing -- something a human expert, such as a teacher, is unable to do. We show that incorporating the dynamic information available by the use of tablet is highly beneficial to our digital test to discriminate between typically-developing and dysgraphic children.

Deep Linear Networks do not have expressive power but they are mathematically tractable. In our work, we found an architecture in which they are expressive. This paper presents a Linear Distillation Learning (LDL) a simple remedy to improve the performance of linear networks through distillation. In deep learning models, distillation often allows the smaller/shallow network to mimic the larger models in a much more accurate way, while a network of the same size trained on the one-hot targets can't achieve comparable results to the cumbersome model. In our method, we train students to distill teacher separately for each class in dataset. The most striking result to emerge from the data is that neural networks without activation functions can achieve high classification score on a small amount of data on MNIST and Omniglot datasets. Due to tractability, linear networks can be used to explain some phenomena observed experimentally in deep non-linear networks. The suggested approach could become a simple and practical instrument while further studies in the field of linear networks and distillation are yet to be undertaken.