We explore the behavior of a standard convolutional neural net in a setting that introduces classification tasks sequentially and requires the net to master new tasks while preserving mastery of previously learned tasks. This setting corresponds to that which human learners face as they acquire domain expertise, for example, as an individual reads a textbook chapter-by-chapter. Through simulations involving sequences of ten related tasks, we find reason for optimism that nets will scale well as they advance from having a single skill to becoming domain experts. We observed two key phenomena. First, _forward facilitation_---the accelerated learning of task $n+1$ having learned $n$ previous tasks---grows with $n$. Second, _backward interference_---the forgetting of the $n$ previous tasks when learning task $n+1$---diminishes with $n$. Amplifying forward facilitation is the goal of research on metalearning, and attenuating backward interference is the goal of research on catastrophic forgetting. We find that both of these goals are attained simply through broader exposure to a domain.

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution changes is also fundamentally important to achieve a more powerful form of generalization. In this paper, we attempt to study through the lens of information measures how a particular architecture behaves when the true probability law of the samples is potentially different at training and testing times. Our main result is that the testing gap between the empirical cross-entropy and its statistical expectation (measured with respect to the testing probability law) can be bounded with high probability by the mutual information between the input testing samples and the corresponding representations, generated by the encoder obtained at training time. These results of theoretical nature are supported by numerical simulations showing that the mentioned mutual information is representative of the testing gap, capturing qualitatively the dynamic in terms of the hyperparameters of the network.

Convolution is a central operation in Convolutional Neural Networks (CNNs), which applies a kernel or mask to overlapping regions shifted across the image. In this work we show that the underlying kernels are trained with highly correlated data, which leads to co-adaptation of model weights. To address this issue we propose what we call network deconvolution, a procedure that aims to remove pixel-wise and channel-wise correlations before the data is fed into each layer. We show that by removing this correlation we are able to achieve better convergence rates during model training with superior results without the use of batch normalization on the CIFAR-10, CIFAR-100, MNIST, Fashion-MNIST datasets, as well as against reference models from "model zoo" on the ImageNet standard benchmark.

The level sets of neural networks represent fundamental properties such as decision boundaries of classifiers and are used to model non-linear manifold data such as curves and surfaces. Thus, methods for controlling the neural level sets could find many applications in machine learning. In this paper we present a simple and scalable approach to directly control level sets of a deep neural network. Our method consists of two parts: (i) sampling of the neural level sets, and (ii) relating the samples' positions to the network parameters. The latter is achieved by a \emph{sample network} that is constructed by adding a single fixed linear layer to the original network. In turn, the sample network can be used to incorporate the level set samples into a loss function of interest. We have tested our method on three different learning tasks: training networks robust to adversarial attacks, improving generalization to unseen data, and curve and surface reconstruction from point clouds. Notably, we increase robust accuracy to the level of standard classification accuracy in off-the-shelf networks, improving it by 2\% in MNIST and 27\% in CIFAR10 compared to state-of-the-art methods. For surface reconstruction, we produce high fidelity surfaces directly from raw 3D point clouds.

Radar-based road user classification is an important yet still challenging task towards autonomous driving applications. The resolution of conventional automotive radar sensors results in a sparse data representation which is tough to recover by subsequent signal processing. In this article, classifier ensembles originating from a one-vs-one binarization paradigm are enriched by one-vs-all correction classifiers. They are utilized to efficiently classify individual traffic participants and also identify hidden object classes which have not been presented to the classifiers during training. For each classifier of the ensemble an individual feature set is determined from a total set of 98 features. Thereby, the overall classification performance can be improved when compared to previous methods and, additionally, novel classes can be identified much more accurately. Furthermore, the proposed structure allows to give new insights in the importance of features for the recognition of individual classes which is crucial for the development of new algorithms and sensor requirements.

Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturbation are inevitable. A concentrated space has the property that any subset with $\Omega(1)$ (e.g., 1/100) measure, according to the imposed distribution, has small distance to almost all (e.g., 99/100) of the points in the space. It is not clear, however, whether these theoretical results apply to actual distributions such as images. This paper presents a method for empirically measuring and bounding the concentration of a concrete dataset which is proven to converge to the actual concentration. We use it to empirically estimate the intrinsic robustness to $\ell_\infty$ and $\ell_2$ perturbations of several image classification benchmarks.

We propose GraphNVP, the first invertible, normalizing flow-based molecular graph generation model. We decompose the generation of a graph into two steps: generation of (i) an adjacency tensor and (ii) node attributes. This decomposition yields the exact likelihood maximization on graph-structured data, combined with two novel reversible flows. We empirically demonstrate that our model efficiently generates valid molecular graphs with almost no duplicated molecules. In addition, we observe that the learned latent space can be used to generate molecules with desired chemical properties.

An important problem in forensic analyses is identifying the provenance of materials at a crime scene, such as biological material on a piece of clothing. This procedure, known as geolocation, is conventionally guided by expert knowledge of the biological evidence and therefore tends to be application-specific, labor-intensive, and subjective. Purely data-driven methods have yet to be fully realized due in part to the lack of a sufficiently rich data source. However, high-throughput sequencing technologies are able to identify tens of thousands of microbial taxa using DNA recovered from a single swab collected from nearly any object or surface. We present a new algorithm for geolocation that aggregates over an ensemble of deep neural network classifiers trained on randomly-generated Voronoi partitions of a spatial domain. We apply the algorithm to fungi present in each of 1300 dust samples collected across the continental United States and then to a global dataset of dust samples from 28 countries. Our algorithm makes remarkably good point predictions with more than half of the geolocation errors under 100 kilometers for the continental analysis and nearly 90% classification accuracy of a sample's country of origin for the global analysis. We suggest that the effectiveness of this model sets the stage for a new, quantitative approach to forensic geolocation.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on the well-known M4 competition dataset containing 100k time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on the M4 dataset strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without loss in accuracy.